I'm looking for a cheap little console I can put in my bedroom and play on my 20-inch monitor, and I don't want to bring my 360/PS3 into the room (usually my parents or family will be watching a Blu-Ray film on the PS3... or playing Rock Band) so I'd like a nice last-gen console with some good games that I can play, maybe before bed or something. Got any advice on that?

Have you got a PS3 with the backwards compatibility chip? If so then go for an xbox since any PS2 games would work right on the 3 and you can buy them whenever. If not then go for the PS2 because it has a lot more games. Then again I thought most of the games on the xbox were better than the PS2 which is the reason I never got a PS2. Suppose its a matter of what will get you the games you want
Oh wait, you can softmod the xbox and make it into a media centre PC which frankly is too damned cool an option to ignore, you can also use that to keep your secret stash of hentai tentacle porn safe from accidental discovery

I do have one of the launch day units, so I do have a backwards-compatible chip equipped PS3. But like I said, I'd rather have a cheap console for my room that stays there permanently, rather than lugging the PS3 back and forth or going to the living room and whatever.
The Xbox's media center hack looks enticing, but I already have a desktop with Boxee running in my room so it's sort of redundant. I did check the list of games the PS2 has, and while it's got more games and it's STILL more popular than the PS3, it's way crappier in visuals compared to the now-discontinued Xbox. Then again, I don't care if it's discotinued or not.

I vote for PS2.
Xbox is better in visuals but it doesn't have a lot of really interesting games. Ninja Gaiden, Halo, Conker. PS2 on the other side has lots of games, exclusives, etc. And if you're interested in jRPGs - PS2 has a lot of them.

Personally I'd go for a Playstation 2, the games were way more inventive and interesting to play. Look at Okami, Shadow of the Colossus, God of War, Ring of Red, Forbidden Siren etc. Plus you have the even more games to look forward to as Sony are releasing 100 new titles over the coming year.

I've got a modded Xbox with the media center, and it's awesome. And since I have an Xbox, I obviously play games on it, and I'm obviously biased towards it, as far as consoles go. So I sayeth Xbox.
EDIT:
And peculiarly enough, not any of the games that Romulus mentioned has ever caught my interest, simply because I'm not a fan of the gameplay style. Maybe Okami, but that truly is a big 'maybe'.
EDIT2:
There are actually quite a few games on the PS2 I'd like, but none of them has to my knowledge been released outside of Japan.

I vote for PS2 also.
A lot of XBox games have been released on PC, if you want some more original games, the PS2 seems the good choice.

Well you can't really go wrong with either, I had an Xbox (well I still have it I just don't use it very much), so maybe I am a little biased towards it. PS2 is excellent as well but it really depends on what kind of games you like. Xbox had more in the way of shooters and Bioware RPGs, while I think the PS2 had more JRPGs and hack and slash action games. Either way there is bound to be somthing for you to enjoy.
Both have some excellent games, but I am going to have to give into my bias simply because of Ninja Gaiden/Black. That game holds the record for most time I have ever wasted on a single game, aside from maybe Diablo 2. Untold hours were spent beating all the difficulties and the various missions, and completing it all was one of the best times I've ever had in a game. Ahh, such fun... such frustratingly fun times.

Definitely PS2 in my opinion. I own both, and the game library of the PS2 is quite a bit better, especially if you like RPGs and more inventive games, as aleks.nt and Romulus said.

As much as I dislike ol' Sony, a PS2 for its library of titles.
Or you have the cash; you could get both, stack them and hook them up to a simple AV switch box (feed quality unrequired on 20") should the telly lack the ports. Toggle to your system of choice and play. Used to do this with my MegaDrive/Saturn/DVDplayer stack, hidden behind the TV.

PS2. You can play the Harvey Birdman: Attorney at Law game on it, so it automatically wins.

I think I have that on PSP.

OK, then. God of War is on the PS2. Get that.

Sounds interesting... though KOTOR is on Xbox! Damn.

KOTOR 1 and 2 are both available on PC, as are most Bioware console RPGs.