IGNORE ME - ONLY 145 POSTS BEFORE THIS!
I want to answer anyway, even if you don't count this. You didn't forbid doing this, so...
I own the 60 GB model and I find PS2 compatibility very important to me. I play on an old SDTV and it has only one SCART plug so I can't keep my PS2 connected at the same time as PS3. It's also pretty annoying to mess with the cables (even if there are only two) so I'd really prefer using only one console. Luckily for my, almost all of my PS2 games work perfectly (well, I haven't tested them all but most of the ones I've tested work); still, there are problems with a few (only minor issues, though).
As for what comes to PS1 games... Apparently they all work (except for some odd exceptions that didn't work even on my PS2) so it's not a big deal. Well, Metal Gear Solid: Special Missions doesn't work but I think that's only because it needs to check if I have MGS1.