A lot of people feel that asking locals is the best way to find out what areas or activities are safe but I don't agree totally.  My rule of thumb is that if the locals say something is dangerous, then it should be avoided because it probably is dangerous.  However, just because local residents say that something is safe does not mean that it is.  Especially in poorer areas or dangerous areas, many locals develop a sort of fatalism.  They have no choice but to live with the danger or problems so they push it out of their minds and get on with their lives.  People in Israel still ride buses but you probably shouldn't and people in Cambodia still farm their fields but you shouldn't walk off the road.  In some areas there is also the problem of racial or ethnic differences that may make it perfectly safe for a local to be there but an outsider is far from safe.  What to do about it all?  By all means ask the locals, they are valuable sources, but also check out government warnings such as those from the US Gov't or from the British Gov't; check with your nation's embassy in that country, most have a person designated to deal with their citizens; and ask foreign workers such as English teachers or Peace Corps workers.  Many people discount the State Dept. warnings as overly cautious or "wimpy" but keep in mind that they have access to information and sources that you do not.  Also, do not trust the press to give you an accurate idea of the crime rate; even countries with free press often suppress crime news in a bid not to lose tourist money.  Also see "Money" and "Your belongings" below for more information.

Take less than you think you will need. I am not going to try to give a list of what to take because what you need depends on what you're doing and where; besides there are plenty of lists on the net.  But unless you are doing specialized travel, e.g. climbing, mountaineering, documentary filming, then you won't need much.  Lay out everything you think you will need and make a budget for how much you think you will spend.  Then take half as much stuff and twice as much money; 1/3 as much stuff and 3 times as much money is even better.  Then pack your stuff in your backpack (and take a backpack, don't use a gym bag or roller bag) and carry it around the block a few times and up and down a few flights of stairs.  A lot of people say it really doesn't matter how heavy your bag is since you don't carry it much but I don't agree.  Even having to go around a large airport when they keep changing your gate number and waiting in line can add up very quickly.  Plus, the more stuff you start with the less cool things you can buy.  Money is the most important thing aside from paperwork and medicines.  If you lost your whole pack as long as you have money and ID in a safe place (example - waist belt, leg belt) you'll be fine.  It may suck big time but you'll live and be able to keep traveling.

Assuming you know where you want to go, the big issues are packing (see above), travel documents, plane/train tickets, and health issues.  Things like where to stay and what to see can almost always be worked out on the ground unless you are going to a region with special requirements like Tibet.

Travel docs- GET A PASSPORT! I don't care if you are a US citizen and can travel to Canada, Mexico and the Caribbean without one, DON'T.  They are not that hard or expensive to get so just get one.  If you ever need your documents replaced, the US Embassy can help you fairly easily to replace a stolen passport but a stolen birth certificate and photo ID are a pain in the butt to replace.  Having a passport also legitimizes you as a traveler- it makes it easier to return to your home country, it is required for most int'l travel, and it can allow you to stay in hostel in your home country.  I find I am treated better at airports when I travel on my passport domestically than on my driver's license (just my experience though).  Other travel docs you may need are visas which you get from either the embassy of the country you will visit before you leave or at the airport/border crossing on entry.  These are more of a pain in the butt to replace than the passport they are in, so keep tabs on it well.

Make a photocopy of everything including visas and give one copy to a trusted person at home, carry one on you in a different place than the originals and if you have access to a scanner, email yourself scanned color copies.  Then, even if both the originals and the copies with you are lost/stolen you can simply go to any net cafe and print new ones to take to the embassy.  If you were in really dire straits, the Embassy may even help you go online there to print them (like if you lost every penny and couldn't afford even a net cafe).

Tickets- use the web for air travel at least to get an idea of prices.  I use the web for tickets anytime I am flying a simple route (one way or round trip) on a normal ticket. If you are looking for an open-ended, year long ticket or a round the world ticket you are likely better off using a travel agent.  Try Expedia, Southwest Airlines (US domestic only), Cheap Seats, and if you are willing to be very flexible, Priceline.

Health issues- get insurance.  This is very important in two cases; travel to countries with underdeveloped medical systems where you may require treatment at a private hospital at high cost or evacuation at even higher cost, and in the United States which has some of the world's most expensive health care.  However, you need it for any country.  Getting health insurance varies a lot by where you live/are from and why you are traveling e.g. students so I can't help anymore than this.  Go online to the CDC to get traveler health info for the each country and region you will or may visit.  Many vaccinations take several weeks to take effect or cannot be given at the same time as others so plan early- at least 8 weeks ahead of travel is good.  Also make sure your childhood vaccines are up to date, for example, if you had the tetanus vaccine more than 5 years ago, get a new one before travel even though it is normally every 10 years.  Many people in high risk jobs get one every five years and it is perfectly safe. You may also need other booster vaccines depending on when you were born. Other standard vaccinations are the Hep A and B which can be given together and are now routinely given to children before entering school in the US but weren't just a 10 or so years ago.  Malarial medicine is another popular topic for travelers to talk about.  Its necessary in many parts of the world.  Options are Malarone (brand name), doxycycline, Mefloquine (brand name), Chloroquine (brand name Aralen®), Hydroxychloroquine sulfate (brand name Plaquenil®).  What you should take depends on where you are going and your own health.  I do not recommend Mefloquine though but I have taken doxycycline (a broad spectrum antibiotic) with no side effects and the added benefit of preventing some food borne illnesses.  It really matters where are going though so consult the CDC and/or a tropical diseases expert.  The drugs are usually much cheaper outside of the US.

While anyone can have initial trouble adapting to a new environment, especially one very different than their home country, true culture shock tends to come somewhere at the 3-6 months period of being in a country or small region.  At that time, you can't blame your feelings on not being able to figure out a menu or buy a train ticket but have to realize the deeper differences.  After one particularly annoying day, you will come home and feel like "I hate this place, I am sick of being 'the foreigner', I hate the food, all I want is a real ____ (fill in the blank)."  Your funk could last days or weeks or if you truly dislike where you are, you may not get out of it till you leave.  But it can be worked through most of the time and if you get back culture shock you will gain an insight into your new home far better than if you hadn't gotten to that point.

Some things I have found to help me get past those bad days are:

McDonalds- I know, in America I never eat there, but there is something about a Big Mac all greasy and fatty and a big pile of salty fries that can get me through weeks of rice and more rice.  Plus there's easy picture ordering so you won't end up with squid when you wanted soda.  Although I did ask for a "Biggu Macu" one time and get chicken nuggets.  This holds true for KFC, Burger King, and especially Baskin Robbins.

Instant messaging- better than email, it feels almost like a phone call.  Spending an hour talking with someone from home has made me feel ten times better than sending an email and hoping they reply.  Try to line up a weekly (or even more often) time with friends or family to talk online.

Exercise- the same way a good run or football game can work off the stress at home.  If you are going to be someplace for awhile (studying, teaching etc.) try joining a sports club or getting into the local sports scene. A few friends of mine ran marathons in Korea and others joined the football team; not only is it a great way to get rid of depression but they made tons of new friends through shared interests.

Change of routine- when I was working 50 hour weeks in Barbados I was getting kinda sick of the place. But when I took a weekend to drive around the coast, I saw a new side of the country and really enjoyed it.  I came back to work the next week re-energized and ready to work.  If you are constantly doing the same thing, whether it be traveling (e.g. always on buses, trains) or going to work, it sucks.  Change your direction even if it doesn't fit what you had planned or even if it is just a little thing like trying a new coffee shop or taking a different bus to school.  Sometimes its the hardest part, but if you are unhappy where you are, do something about it !

Getting a routine- it's kinda the opposite of changing things.  Think about what makes you feel at home when you are at home.  Is it getting up each morning and watching the news with a cup of coffee? Or going for a jog each evening?  You don't have to re-create the activity in your new location, just find something that fits the theme.  When I traveled in Southeast Asia I made it a point to get up early and go for a coffee at a small cafe every  morning.  Didn't matter what cafe but I kept this habit through several countries.  Throughout I was well caffeinated and I had gotten a better look at the cultures I was in than I would ever have gotten by going out all night and sleeping in.  Eating routines are very important also because your body needs them along with your mind.  Try to keep to a regular schedule for mealtimes and the physical difficulties of lots of travel will be lessened.

Toilets
Carry toilet paper with you everywhere.  You can take the cardboard tube out of a whole roll and put it in your pack then take a bit with you when you go out and about.  In many countries you can also buy tissue packs that are very handy.  In less developed nations you will almost never see toilet paper in the restrooms but even in Korea it is only sometimes supplied in bars, restaurants etc.  Also make sure you know what to do with the toilet paper after use, plumbing in many places is inadequate so there is usually a trash basket by the toilet.

Get rid of expectations of privacy.  Think about it - you may be freaked out at the idea of "visiting" a field while on a long bus trip but consider how much more sanitary that field is than the outhouse with two wood planks over the pit.  You will quickly learn to love the field.  Also, if you are a woman, do what the locals do and wear long, full skirts when traveling.  That takes care of the privacy issue fairly well.  Men, quit your complaining and be glad you aren't women.  Another time you can't expect privacy is in many parts of China and Vietnam.  Chinese style restrooms usually have either no doors on the stalls or half doors that don't lock.  Either way the foreigner using the toilet will end up being a source of much amusement for the locals, even in a fairly cosmopolitan place like Beijing.  Many westerners try to use the last stall in the restroom to limit the number of people passing by but again, think about it: everyone is trying to do the same thing so 10 times as many people are using the last stall than the first, consider the effects of that.  In many places, be prepared for the toilet to be missing major components such as seat and pipes.  If there is a bucket of water next to it with a scoop, that is what you use to flush the toilet.  In Asia, also be prepared for "asian style toilets" aka "squat toilets."

Look for good sources of clean facilities and use them every time you see one.  Top of the list is usually American fast food chains like McDonalds, Burger King and Pizza Hut, all of which will let you use their bathrooms for free (other restaurants like Bennigan's have nice toilets but they're usually for customers only). Next are nice hotels, anything like the Sheraton or the country's equivalent.  These may be for guests only but as a foreigner in a non-western nation no one will question your using the lobby restrooms.  After these comes local upscale places.  After that all toilets are a lot alike- they vary from bad to worse.  On bus trips, if it is safe to do so, consider making a trip to the bushes rather than the truck stop outhouse.  Your senses will thank you for it.  However, please be considerate of nature, e.g. don't leave trash behind, be at least 200 meters from a body of water.  One way to judge if it is safe to do this is to watch local women of about your age.  If you must use bad facilities, try carrying the alcohol based hand gel or alcohol wipes for hand "washing".

Money

Unless you have been there before, don't expect credit cards to be accepted all over.  Most any median income or less country is a cash society and Asian nations also tend to be cash only.  Businessmen in Japan and Korea routinely carry hundreds of dollars (obviously not dollars but you get the idea) in cash when they go out to restaurants and bars.  Credit cards though are a necessity for a traveler, carry at least one either of Visa or AmEx.  If you are a couple, each carry one card of a different type, preferably ones with "cirrus," "maestro," and "plus" on the back.  Find out from your bank the options for getting cash from your card and the legal protections of using it. Make sure your PIN can be used abroad and know the numbers since many ATMs outside of the US do not have letters on them.  Also, if you are going on an unusual (for you) trip- country hopping quickly, making large purchases, or getting large amounts of cash, it is good to contact your card issuer and tell them so they do not put a freeze on your account because of "suspicious activity."  There are ATM finders on the web for different cards, although they do not list every ATM, they are worth looking at.

I suggest having 3 different types and sources of money- basically a credit card (better than debit for theft protection), some travelers checks (maybe 20% of your budget), and cash.  Replenish the cash every two or three weeks using the credit card.  Cash advances are available in most major cities and the fees are usually not more than you would pay for ATM use or the fees for cashing travelers checks.  Split your money up and keep a small amount in a pocket to use for little purchases throughout the day.  NEVER get into a money belt or any hidden stash in public.  Excuse yourself to the restroom instead.  The amount in your pocket is also security against robbers- hand over a dummy wallet containing some cash and maybe an expired credit card.  Some people also suggest throwing it and loose cash to the ground to give you a chance to get away.  Don't get freaked out though, robbery like this is fairly uncommon unless you are someplace you shouldn't be (and these places tend to be fairly obvious).

US dollars are the way to go almost everywhere.  Euros are gaining acceptance though and pounds and yen can be changed in most major cities.  But for changing in small towns or outside of banks, $$$ are it.  Change a fair bit at a time, larger bills get better rates and then use the local currency.  You will get a better exchange rate and it will be easier to shop and eat in small places that either don't take $$ or cannot give change.  I've eaten in many places where a whole meal is less than a dollar and if I had handed them a US $10 they'd never know what to do with it.

Your belongings

When you are travelling by public transportation, DO NOT let your valuables bag out of your sight and preferably also, touch.  Meaning, always have physical contact with your carry-on bag and keep an eye on it whenever possible.  I prefer to either have my bag on my lap or sitting on the floor, tucked between my legs.  This way I can both see it and feel if someone tries to move it.  If I wish to sleep, I put it on my lap and rest on top of it, then it becomes very hard to steal or steal from.  DO NOT put your bag up on a rack in a bus and then fall asleep, there is a good chance it will "walk away" or something will go missing from it.  This is especially true around the times when people are getting on and off the bus or train because it is easy for someone to just grab your bag like it is their own and walk away.  Some countries are worse for this than others and it is not always related to the affluence of the country, ask around and be careful until you know more.  Suitcases and backpacks that are locked and placed under buses are generally okay; if it goes on top of the bus, make sure it is locked and/or in a sack to keep out idle hands.

In hotel rooms, keep most of your stuff in your bag.  While people are generally honest, nice things lying about, especially money of course but also things like watches, can be very tempting for someone earning a dollar a day.  You'd think this would be obvious but it is not.  Depending on the country, either take your camera etc. with you when you leave the room, lock it in an in-room locker or safe (preferably with your own padlock, not the hotel's), or put it in the hotel safe making sure to get a receipt.  Things left with the management of reputable hotels are generally safe.  If it is small items like a passport or money you are leaving, put it in an envelope and sign your name, and have the management sign theirs, across the seal so it will be obvious if it has been tampered with.

When out and about, carry a small shoulder bag or purse.  A messenger bag or army medic type bag is good for men who probably don't want to carry the latest leather clutch.  You can carry it across your shoulders or on one, but whichever you should carry it towards your front and preferably with your arm lying across it.  Small backpacks are great for day hikes or other places where a lot of walking or climbing is involved (ex. Angkor Wat, the rainforest) but not very good for cities as you cannot see or feel your stuff, making it vulnerable to thieves with razor blades.  Don't be paranoid, just be aware.  Thieves look for easy targets.  Knowing common scams/ practices in each country you're visiting is valuable: ex. in Costa Rica, theft on buses is widespread (enough to warrent signs in multiple languages on the buses) while in Italy a trick is to "acccidently" put mustard (or mayo etc) on your clothes and help you clean it off while someone else lifts your wallet/bag/whatever.  In general, be wary of anybody trying to help you clean something off your clothes or pointing a mess out to you.  They may be perfectly honest but it isn't going to hurt you to wait and visit a restroom to clean up.