Cannonball and TGBDual still have have their issues, and Fuse most likely does too (I don't like purposely freezing the PS3).
Virtual Jaguar is still painfully slow.
81 sorta works...I got several games to boot, but no controls worked. Like DOSBox, you are supposed to map the RetroPad buttons to keyboard keys (via Core Options), but it doesn't seem to work. Need to do more research here.
O2EM now has the 1, 2, 3, and 4 keys mapped to Square, Triangle, L1, and R1, respectively - use these to get past the Select Difficulty screen. Tried 4 or 5 games, all worked, guess this core can be called stable now.
GME (Game Music Emulator) plays video game music, only tried 1 NSF file (SMB3), worked. Start to play/stop, L1 and R1 to change tracks.
Haven't gotten around to Mednafen SuperGrafx or Mednafen Lynx, but these previously stable cores *should* be fine. Speaking of the Lynx - we know that some games work on one core but not the other, but I have NEVER gotten the Handy core to work - every game I've tried froze the PS3. Anybody know what game(s) work with Handy?