Being constantly on the move for three months straight can be difficult, especially when you're in another country. This is just a list of hints to make things easier for you.
Immerse yourself in the culture (read: food). Cuisine is often one of the most integral parts of a culture. Have tapas in a Spanish bar at 22:00. Order the roast duck in Prague or the steak frites in Belgium. Get a croissant in the morning from a French bakery. Sure, McDonalds are everywhere and they're usually cheaper than local food. But it would've been easier just to eat fast food back at home.
Speak the language...or a few words of it, at least. We've been to 10 different countries, and many times a country will have more than one language. It's impossible to always speak the local language, but David '12 and I try to memorize simple salutations, phrases, and numbers. (Hello, please, thank you, goodbye, and 1, 2, 3 are usually enough.) People really will be infinitely more helpful if you make an effort to communicate on their terms.
The US has a tendency to "Americanize" things. For instance, alfredo sauce isn't from Italy - it was made by an Italian guy who came to the States. So when you ask an Italian for alfredo pasta, they look at you strangely. :D
Be an extrovert. Meeting people is the spice of traveling, and the best way to meet locals is to get out of the touristy areas. Knowing people can help - we knew someone who took us to a party in the catacombs under Paris!
Look at things with an engineer's eye. I've gotten a really interesting look at engineering by traveling Europe. People here have come up with much different solutions to problems than we have in the States, and there are always more problems that need to be solved. Example: Water usage can be a problem, especially with toilets. Engineers here have simply introduced a "high flush" and "low flush" system, with a button for each above the toilet. It's much more efficient.
Appreciate the history. I'm not one for history myself, but the fact is that the cities of Europe are much older than most places in America and each city has a significant history behind it. Being there can make it a lot more interesting - learning about the Berlin Wall was one thing in high school. When I saw it in person, though (or what was left of it), the crumbling wall really made me think about the hundreds of people who tried to escape over it.
Pack the right equipment. Ordinary things like a compass (useful for getting your bearings), paracord/duct tape (both useful for improvisation), and a foldable bowl might easily be forgotten, but they can make all the difference sometimes.
Don't let your guard down. As much as it's good to meet people, there will always be those who are a little too friendly and want to empty your pockets for you. I keep my valuable documents and money in a money belt - not fashionable but very safe. There are also many popular scams around tourist attractions.
Let go of your inhibitions. My goal was to leave Europe with no regrets, and I can safely say I succeeded. I'd say that's the most important part of any trip, wherever you go.
< Derek >