For CFW PS3s, there's a homebrew PS2 Emulator for PS3 called PS2 Classics Placeholder to play select PS2 games and you use a PC Tool called PS2 Classics GUI to convert PS2 ISOs to a compatible PS3 format. It uses the PS3's native ps2emu to play them.
NTSC(U.S.), PAL(Europe), and NTSC-J(Japan) all work for it
PS2 Classics Emulator Compatibility List List of games confirmed working/not working. Anything else is hit or miss really.
Some games that I played like Yakuza 1/2 had some crash problems at certain points in the story.
Reason some PS2 games never got on PSN's PS2 Classics like the awesome Dot Hack series by CyberConnect