The older games use Z80's (I think stuff like Pacman, Pengo, and all of those blocky non-descript 8-bit games).
After that there's the 6502 based games (stuff like Ghosts 'n' Goblins and I think maybe even Gradius (even tho that pushes its hardware, whatever it is, a LOT) - 6502 games are basically the stuff around 1985. I imagine Bubble Bobble would be in this group.
68000 is the one that is most common in MAME, though. Unfortunately that works against the GP32's favour...I imagine the MAME core is rather unoptimized or something in this aspect. Games that use it include TMNT, the CPS-1 and CPS-2 games, Neo Geo, a few Namco games, Konami-GX games, all of Taito's F series games, there's quite a selection really.
Also I should point out that I doubt Atari arcade games could be run on GP32. The old stuff maybe, but there isn't much there to emulate (Vectors were big for them in the early days and they would look fugly on GP32!). The popular games...everything from marble madness onwards...had a massive and wierd resolution. I think it was 512x512.
So, in conclusion, Z80 games are completely possible. So are 6502 based games. You could do both of these with sound even. 68000 is pushing it, but some of the older stuff I think is possible - perhaps sacrificing sound or using MIDI emulation instead (which would sound horrible!). Just don't expect CPS2, NeoGeo or Taito F3 or Konami-GX emulation. Atari games are a definite no-no.