Downloading Games
The PSP can only legally download games from the PlayStation Network, which does not offer any PS2 games for download as of December 2009.
Emulation
The PSP does not feature support for any PS2 games. The console would require a PlayStation 2 emulator, which does not exist as of the end of 2009.
PlayStation Games
The PSP can play games made for the original PlayStation. The games can be downloaded from the PlayStation Network.
Physical Limitations
The PSP only features one analog stick while PS2 games require two analog sticks to control game play. PS2 games would need to be reconfigured for the loss of the stick.
Reverse Compatiblity
PSP games have later been released for the PS2 such as Secret Agent Clank and Silent Hill: Origins. PS2 games have not been ported to the PSP.
PS2 Game Support
PlayStation 2 games can be played on early versions of the PlayStation 3, while the PSP requires games to be downloaded or placed on a Universal Media Disc (UMD).