One of the bigger questions surrounding the PS3 was how wll the backward compatibility would work. Overall things worked out well enough for PSOne games but some testing has found some PS2 games that do not want to play nice:

• Tekken 5
• Xenosaga Episode II
• Code Age Commanders
• Radiata Stories
• Star Ocean Till the End of Time (includes Directors Cut)
• Driving Emotion Type-S
• Gran Turismo 4
• Hot Shots Golf 3/4
• Operator’s Side
• Onimusha Dawn of Dreams
• Hyper Street Fighter II Anniversary Edition
• Megaman X7
• Devil May Cry
• Onimusha
• Suikoden III
• Silent Hill 2

In most cases there are only minor glitches and are still playable but a few simply refused to oblige. CNet's Japan site reports a total of 196 titles (keep in mind many of those were probably released only in Japan). Sony is reportedly working on fixing the problem through firmware updates or possibly resorting to patching on a game-by-game basis.