the 40GB PS3 NEVER played PS2 games!!! quit telling people that it does!!!!!!!!!!!!!!!!!
backward compatibility for the PS3 with PS2 games is as follows on NTSC systems:
20GB (4 USB slots, fat, no longer in production) - YES
60GB (4 USB slots, fat, no longer in production) - YES
80GB with 4 USB slots (fat, no longer in production, bundled with MGS4 or Motor Storm) - YES
40GB (2 USB slots, fat, no longer in production) - NO
80GB with 2 USB slots (fat, no longer in production) - NO
160GB (2 USB slots, fat, no longer in production) - NO
120GB/slim (2 USB slots) - NO
250GB/slim (2 USB slots) - NO
any other up coming PS3's - NO
PAL systems only have one backwards compatible system, and that's the 60GB.
THAT'S 4 SYSTEMS THAT ARE IN FACT COMPATIBLE WITH PS2 GAMES!!! NOT 1 SYSTEM, NOT 2, 4!!!
in short: if it has 4 USB slots, yes. if it has 2 USB slots, no.
and as you can see, there are 3 systems that are fat, but can NOT play PS2 games. just because the system is fat does NOT mean it can play PS2 games.
ALL PS3s play PS1 games.
http://en.wikipedia.org/wiki/PlayStation_3#Model_comparison
the download that others are referring to is for the PS3s that already are backwards compatible. downloading it to a non-backwards compatible PS3 will do NOTHING but take up space on your hard drive! it will NOT make your PS3 play PS2 games!!!
"If a PLAYSTATION 3 is not backward compatible, you will not be able to add this function through any hardware (i.e., changing the hard disk drive) or software (i.e., updates, homebrew) upgrades or modifications. "
that came DIRECTLY from Sony's own website: http://playstation.custhelp.com/cgi-bin/playstation.cfg/php/enduser/std_adp.php?p_faqid=232&p_sid=1P9bCDwj
I dare anyone to steal my answer again. this is MY answer. I took the time to type this all up. yes, every time someone asks this question, I do copy and paste. but I'm copying MY work, MY answer.
there is no complete list that I know of. I'm sure you might find a list of some kind if you look for yourself online, but if you want to know for sure if any games you have will work on your backwards compatible PS3, check this site: http://us.playstation.com/support/compatiblestatus/