The only PS3s that can play PS2 games are the 60GB (CECHA), 20GB (CECHB), and 80GB (CECHE) models.
The 60GB and the 20GB had full hardware emulation where it had both the PS2's CPU & GPU on the PS3 motherboard. The 80GB only software emulated the CPU, the GPU was still on the motherboard, so it is really software and hardware emulation, not software only emulation. By my estimate the 80GB has severe problems running about 10% of PS2 games.
If you happen to live in Europe their 60GB (CECHC) is the same as out 80GB, emulating PS2 games via software and hardware.
There isn't any other way to find out the model number without looking at the unit, as far as I know...
No, you can't. They've got the technology to do it. The earlier models could do it. But frankly, the truth is they just don't want to. They want your money, and giving you the privilege of playing ps2 games on a ps3 would get in the way of them getting money. After all, if you own a PS2 game and you could play it on the PS3, then how exactly would they get money from the online shops? One fragile excuse for this I tend to hear is that 'Why not just play it on a ps2 then?'
Two reasons. The first one is convenience. Having just a ps3 to play my PS2 games makes it so I don't have to use up a lot of plug outlets. In some cases for people, I can even imagine that they already are using all the outlets, so they have to hook/unhook everytime they want to use it. This, I can imagine, is a real pain. Secondly, a PS2 won't be around forever. So it's always nice to be able to play PS2 games on a PS3 for whenever the system dies. It really gets to me on how a PS2 game could play PS1 games, but a PS3 can do neither. I guess it really can't do everything after all. What probably upsets me most though is that a big part of the PS3 marketing was that it DID have backwards compabitility and that it was, if I'm correct, better than an Xbox's. Now it isn't, because it doesn't have it. And you know, that's one reason I got a ps3. Because I thought it was awfully great to not have to worry for whenever my PS2 was going to die - It was nice being under the delusion that I would be able to play those games even afterwards. I guess not.
It's worth criticizing alone on how I have to rebuy basically all those games (or get a ps2. And I'll probably be doing this because I can do it from a pawnshop where sony -won't- be getting my money. Well, that and it would be cheaper than rebuying all the games) but you know, even if I did choose to rebuild my library by purchasing the games online, that still wouldn't get me all my games back. Sony won't rerelease every game in existence, and some of the games I own they are - quite simply - not the kind of games you'll EVER find a rerelease of. So drawing full circle, I'll again answer your question. No, you can't play ps2 games on a ps3. On an outdated model that's essentially an anachronism you could, but on the brand new 'advanced' model you can't.
I have PS3 the 160 GB version, can I play PS2 games ?
Only the following PS3 models can play PS2 games: