Sony has put up a compatibility list of Playstation 2 games on the support site of Playstation.com. Sony is being a little sneaky and did not actually post a list, you have to search for the title; by searching you really do not know how many titles do not work on the Playstation 3.

A random search of some games revealed the following:

Super DragonBall Z
Publisher: AtariProduct No: SLUS-21442
Description: No major problems for this title.

Superman Returns (M)
Publisher: Electronic Arts
Product No: SLUS-21434
Description: No major problems for this title.

SOCOM 3: U.S. Navy SEALs
Publisher: Sony Computer Entertainment
Product No: SCUS-97474
Description: The title is unable to perform intended HDD functionality