The recently released PS3 in Japan is compacntable with many PS2 games. But due to software problem, no PS2 games that requires PS2-HDD is playable on PS3 currently. The good side is Sony is already planning on fixing this problem in a future PS3 software patch.

Details from an IGN news:

Games that use the hard disk will currently not run. The problem is that the built-in PS3 hard disk cannot currently be used as a PS2 hard disk. We haven?t tried it out ourselves, but this means games like Final Fantasy XI and Nobunaga?s Ambition Online won?t work.

For now at least. The good news is that Sony plans on making hard disk based PS2 games compatible in a future system software update. The list of titles that will work once this magic system update is carried is basically just Nobunaga?s Ambition Online, Final Fantasy XI and the Play Online viewer, and Front Mission Online in all their variations, including expansions.