No they can not be played on any recently purchased PS3. The old 4 USB port PS3s made in 2006 and 2007 could play some PS2 titles, but not as perfect and trouble free as the PS2 does.
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No, only old PS3 Game consoles with 4 USB ports can play some PS2 game titles.
No as the PlayStation 3 Blu-Ray discs are too large to fit in the DVD slot on the PlayStation 2, although you can play most PlayStation 2 games on American PlayStation 3's and around 50% of PlayStation 2 games on European PlayStation 3's.
Playstation 3 can play old Playstation games, but Playstation 2 games are not compatible. You can load some playstation 2 games using the hard drive and an emulator, but not all.
There are a number of video game consoles on the market today that are capable of playing dvds. The Xbox, Xbox360, PlayStation 2, and PlayStation 3 are all able to play standard DVD's.
You can not play PlayStation 3 games on a PlayStation 1, but you can play PlayStation 1 games on a PlayStation 3. All of the PlayStation consoles are backwards compatible.