Yes you can play PlayStation 1 games on a playstation three. All playstation 3's can. However, the 20 and 60 gigabyte versions are compatable with more games than the 40 or 80 gigabyte ones. Also if you find that your play station 1 game does not work on your PS3 look in the playstaion store. they have many PS1 games.
It depends on if you have a newer or older version of the Playstation 3. The original release could play SOME Playstation 1 and 2 games. However, the newest models cannot play your old Playstation 1 or 2 discs at all.