I stayed in Yellow Hostel in Rome, and I really had a wonderful time. They have a really good breakfast (free!) and the net was free, and they had a night tour/pub crawl. Generally I avoid such things, but this one was really cool and helped me get a handle on at least the very central part of the city. I think it cost around 15 euros, but it was worth every cent. The place was a bit odd, but it was clean. The bathrooms were sparkling.
I just got back from Amsterdam, we stayed at Bob's. Its 22 euros a night (maybe more expensive during the high season) and the breakfast was ok. Eggs and toast and tea. The staff was really cool, they seem well versed in the art of keeping an eye on twitching tripping people in the corner without interfering. Its got that awesome old school euro hostel feel (rather than say, the feeling of a shopping mall overrun with kids as seems to be more prevalent). Good international mix. I dont think I would bother staying anywhere else. There's an excellent coffee shop right next door, called "The Doors," and its a good place to get started.
Also, there's a free tour of the city that stops by around 10 am to round up stoners to expose them to the fresh air. Take it. Really, really, take the tour. Its fantastic- interesting but not too many words (made for thinking stoners) and plenty of off-color as well as informative anecdotes. Its free but you'll have such a good time you'll want to tip well.
"All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act their dreams with open eyes, to make it possible. This I did."
-T.E. Lawrence, Seven Pillars of Wisdom