Some info for BlackChocobo...
A handful of PlayStation titles (notably Metal Gear Solid: Special Missions) fail to run on the PS2 at all (Special Missions fails to recognise Metal Gear Solid at the disk swap screen, for example). This problem appears to have been rectified in the slimline versions of the PS2, where most of the previously unplayable PS one games can now be played.
Sony stated every PlayStation and PlayStation 2 game that observes its respective system's TRC (Technical Requirements Checklist) will be playable on PS3 at launch. SCE president Ken Kutaragi asked developers to adhere to the TRC to facilitate compatibility with future PlayStations, stating that the company was having some difficulty getting backward compatibility with games that had not followed the TRCs. It has been confirmed (image) that initial PS3 units will include the CPU/rasterizer combination chip used in slim PS2 (EE+GS) to achieve backward compatibility.[51] Two days after the release of the PlayStation 3 in Japan, Sony announced that some titles had big problems, mostly with sound playback.[52] It has also been reported that some scenes from the Gran Turismo racing game might freeze, the game Suikoden III cannot read data from a first-generation PlayStation, and a virtual gun in one of the Biohazard games will not fire properly.[53] Most of the 7841 titles in Sony's database work; future firmware updates will provide more compatibility. As of November 16, an online firmware upgrade has been posted by Sony that is intended to address some of these issues.[54] PlayStation and PlayStation 2 software will still be limited by region-locking and will not be enhanced or upscaled.[citation needed]

The PlayStation 3 does not include interfaces for legacy PlayStation devices, though IGN.com tested a legacy controller using a PS2-to-USB adapter, finding that it is compatible, though most other devices (such as the Guitar Hero controller) may not be compatible [55]. USB devices for PlayStation 2 may be compatible with PlayStation 3. A memory card adapter is available[1] so users can save their PS1/PS2 data[56] on to a virtual memory card in the hard drive. PlayStation 3 can use Memory Sticks to store save data for PlayStation and PlayStation 2 software.[57]
Both from Wikipedia.