1. there have been previous fatwallet threads on this and related topics - look it up with the search engine, make sure to check the box to see "archived" posts
2. look at the flyertalk.com discussion forum for this and related topics
3. check out ricksteves.com for ideas
4. like the posters said above, use trains to travel within europe. look up rail passes etc. to see all the ways you can do this and the various prices. buy your train pass before you leave the US - much cheaper than waiting until you are there.
5. hitchhiking in this day and age is risky anywhere in the world and i would not advise anyone to do it
6. don't try to rent a car, trains are much better
7. don't forget Coach travel in some countries if you are short on cash - some Coach/long-distance-bus routes in the UK, for example, cost much less than the same train journey, although it is less pleasant and usually takes longer than the train.
8. if you are under 26, there are discounts on a lot of things - flights, train passes, youth hostel memberships, etc. never be afraid to ask if there is a discount. same goes if you are a senior.
9. at least in the UK, youth hostels can be pretty bad, and i'd recommend not staying in them in the UK as a general rule -- and they really are about the same price as an inexpensive hotel, if you know how to look. however, in germany, austria and switzerland the quality is much higher, typically. if you are not young, you can still stay in hostels and pay a bit extra. also, they often have private rooms for a higher nightly rate, which can be much more relaxing and safe-feeling than staying in a bunk-bed dorm situation.
10. have fun! beautiful places, beautiful time of year.