The PS3 has a wide variety of games and a list of the PS3 games has been added under the related links
Every ps3 can play both ps1 and ps3 games. Some models of the ps3 can also play ps2 games.
see related list
It would depend on what kind of games you play.
You need a console to play console games. Computers play computer games and a PS3 will play PS3 games or the Same for the Xbox 360 and the Nintendo Wii.
It all depends what kind of ps3 you have. If you have an older 60 GB then yes you can play ps2 games on your ps3, but these ps3's are not being manufactured anymore. So if you bought your ps3 right when they came out and it's a 60 GB, chances are you can play ps2 games in your ps3, but if you more recently bought your ps3, then most likely it wont play ps2 games.
All PS3 models can play PS3 games and also select PS1 games
well the Call of Duty games,Tekken, Madden NFL i cant think of anymore but there are a lot
no you can download just ps3 games on you ps3
A PS3 can play PS3 games and some Playstation games
there are no Pokemon games for ps3
No PS3 games require a PS3 platform
PS3 games are supposed to be region free