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The 360 can play some Xbox games. I don't remember how many, but when the 360 came out, they would increase the compatible Xbox games list with updates.

The launch 20gig and 60gig PS3's (NTSC at least) have full (or nearly full) PS1 and PS2 backward compatibility. Later, they had the 80gig PS3 which could play most PS2 games due to the removal of the PS2 CPU though I don't believe PS1 emulation was affected. Now, they've removed all PS2 backward compatibility with the 40gig and new 80gig (40gig PS3 with a bigger HDD) though PS1 backwards compatibility shouldn't have been affected. Lastly, I don't know if that 160gig PS3 has PS2 compatibility or not. This is just hardware compability though.