I agree with Greg on every point. I might add that Eastern Europe is generally less expensive, or so I have heard. I might also throw in Amsterdam in the list of cheap airports, and I definitely agree that a Eurorail pass is generally not worth the price.
I first began traveling at the age of twenty. I sold my car at the time, at a terrible loss, took what meager savings I had and set off for a month in Europe. I had no camera, very little money, and traveled almost exclusively by hitchhiking. Granted, I did not eat terribly well, and usually slept in the great out-of-doors, wherever I could find a spot (fields, park benches...I am not advocating this style of travel by the way), only occasionally taking a room in a hostel, and a simple hotel for two nights in Paris.
I found hitchhiking to be a wonderful way to meet people. I traveled from England to France and onto Italy, Switzerland, and Belgium, then back to England. It was a bit of a whirlwind trip, but I was driven at the time, and even managed to squeeze in a great many museums and other sites. Bear in mind that this was a terribly ascetic method of travel, but also quite rewarding.
I recall a great many incidents of generosity and good will. My first ride was with two young French guys, both drunk, who gave me a rather warm beer (which spewed all over when I opened it). An English truck driver let me sleep in the car he was pulling and then shared his breakfast of coffee and ginger snaps with me. A Swiss family was just closing up their restaurant in Geneva when I happened by and they invited me in, fed me a wonderful meal, and supplied me with a bag full of chocolate, cheese and bread, all gratis. I was hitchhiking with a fellow from Slovenia once and an older Italian gentleman picked us up. He dropped off my fellow traveler first, then took me to his home in Asti, where his wife cooked me a meal and I had a wonderful conversation with his college age daughter and her boyfriend. An American photographer living in Geneva bought me a hamburger once, and advised me not to sleep on the street.
And who can forget being dropped off at 2 A.M. by a French truck driver in the middle of Paris, and having no idea where I was?...
Also, please bear in mind that this was back in 1994.