Dirt-cheap rooms, but a lot of time you have to sleep in a bunk bed with some random stranger above you. As few as 1 person in a room to as many as 20. In Munich they had a massive tent you could stay in--probably 75 people in it. Some of the hostels also had private rooms.
Don't expect anything close to fancy. But it's a fantastic way to meet people. Most are between 18 and 25 in the hostels.
I could've hooked up two other times (once with this hot little Asian-looking number from Kansas, and another time with a lanky tall dutch babe), but oddly enough I was dating somebody in the States and didn't want to cheat on her. I finally realized how dumb it was and I dumped the American girl via email. Two days later I met my wife. Good call on my part.
Go buy a budget travel guide book like Let's Go Europe or The Lonely Planet. I went two months in Europe, spending around $7k in all. (That was in 1999 with a stronger dollar, though.) Did the Eurail Pass, which was way cheaper than renting a car. Man it was fun to wake up in Brussels and just decide to go to Paris on a whim.
Whenever I see some 20 year old kid driving a $25k car, I just want to shake them and say, "Sell that fucker, drive a $2k clunker, and with the money you save get on a fucking plane to Europe. Ten years from now you'll barely remember the car, but you'll sure as hell remember feeling up the cute little Brazilian chick under the Eiffel Tower."
