Whatever your mode of transportation, these tips will help to guarantee a rewarding trip abroad.
Packing

Pack light. Rather than lugging two weeks of shirts and underwear to the other side of the world, wash your clothes! You should be able to fit everything for a two-week trip in a big backpack (get one with an aluminum frame) and a shoulder bag. Wear the sports jacket, instead of using specialised luggage.

Travel Photo

Travelers moving around need bring only one suit or dressy outfit, if one will be needed at all. Otherwise, you'll end up wearing your favourite sports jacket every time and lugging the others around for nothing.

While books are heavy, I tend to do a lot of reading when traveling. An excellent option is to buy a used Apple Newton or another palmtop computer, and download some electronic books. The batteries last for weeks and weeks of heavy use. Try to pick a model with back lighting.

Bring a swiss army knife, buying one if necessary. A bit of picnic equipment, such as an insulated bag, some paper towels, cups, and the swiss army knife is all that is needed to turn 10 francs worth of baguettes, wine and cheese into a great lunch.

Clothing

Wear sensible clothes. If venturing into hot climes, pick clothes made of lycra or polypropolene or goretex, rather than Evil Cotton, even if you wan't be on your bike. Cotton soaks up sweat, rather than evaporating it, and makes you hot and uncomfortable when you shouldn't be. Advanced fabrics should be like a second skin. You'll have to spend a bit, but do so.

If you're riding, use a sports bra. Otherwise don't wear a bra in hot climates, because 95% of the locals who don't need to, don't outside of North America.

For those on bikes, look for touring bike clothes when expanding your cycling wardrobe for the trip. Pockets, less of a spandex look, and other features make them more practical than racing clothes.

If comfort dictates, don't be afraid to show a little skin. People are only puritan and irrational about the human body in North America and in some parts of the Muslim world. On the other hand, I need to learn that when riding in just cycling shorts (I'm a guy), sun block is required -- a flat back doesn't get shade on the return trip!

When in Rome, Do as the Romans Do

Never eat within two blocks of an American-owned hotel when abroad, or in any other touristy area. Don't spend 400 francs for crappy tourist food along the Champs D'Elysee. Rather, visit a small-town bakery and pick up some real bread, real cheese, ridiculously inexpensive wine, and mineral water, all but unavailable in Southern Ontario, for a total bill of about $3, eating while overlooking a breathtaking valley along the side of the road. Inquire about the local specialties. You could eat McDonald's food without leaving the comfort of your own town, remember.

Experience the local way of life. Visit a department store. I was stunned by the electronics, cars, household appliances, and even foodstuffs available in Europe, which makes North America look like the Sudanese outback. The items noted are at least 5 years ahead outside of North America, with sterile milk which doesn't need refrigeration and cars that you'd think have to be secret prototypes stolen from a research lab. It's an enlightening experience to see this first hand.

Experience the local haute cuisine. Toronto isn't old enough to have a real cuisine of its own, so dining at three star resturaunts (or even Michelin one star!) totally knocked my socks off. Cooking is an art form, rather than an act of vulgar subsistence as in North America. Experience this, and learn from it.

Socialise with the Locals

Go to a local bar, or drop by a park, or whatever, and meet some people. They'll be happy to meet you, and will be very hospitable. There are some aspects of the local culture that one simply cannot get a handle on by window shopping at noon. Don't think this includes going to some night club full of American tourists beside the Holiday Inn.

Make your very best effort to speak the local language or dialect. Many speak English, no matter where you are on the globe, but don't start off by forcing them to conform to your language and customs! Stumbling through a few words in the local language before the clerk smiles and the conversation changes to English will make a huge difference in how people treat you.

Try to learn from people. Ask about local politics. People will be all too happy to explain and share their opinion about the farmer's strike or what the ECU means to Eastern Europe, about where the farthest view or tastiest bread is found, or about local customs and beliefs.
Learn in Advance

Read about where you're going, before you get there. It's hard to make meaningful insights if you are still catching up from the homework you didn't do the month before on the basic elements of life, culture and history. Get a Michelin guide book (they're excellent, have all sorts of context and detail) for all of the regions you'll be visiting, and read about them before you arrive. It will increase the value of the trip tremendously. Read the encyclopeda article about the country, as well.

Be Subtle

Do not carry a camera around with you. You will be branded immediately. Don't flash big wads of money around. Keep a low profile with your camera, especially around begging children, who will swarm on you, demanding that a picture be taken of them, too, and beg for handouts of money and food. (If you don't like this, write to the IMF and other US corporate policy organisations, and tell them to stop impoverishing the world.)

Be aware that Americans are known around the world as imperialist, black-hearted swine, who exploit the world's population to their own selfish ends. While you may just be a nice guy who shows up at work and rides his bike around a bit, the exploitive economic imperialism bit happens to be quite true, and people know it. If you are American, sew little Canadian flag patches on your backpacks and the like, or people will attach lots of negative stereotypes to you.

Be extremely careful about your passport. Keep in in your inside pocket. Don't keep all of your money in the same place! If you're going outside of the developed world, carry a range of currencies and travelers' cheques.