PlayStation / PS1Edit
See PSP Eboots.
Game Boy AdvanceEdit
TempGBA4PSP is the most recent GBA emulator for the PSP, and has superior compatibility with most problematic games (Golden Sun, for example).
GpSP is an open-source Game Boy Advance emulator created by Exophase and is probably the best Gba emulator on the psp.
Game Boy / ColorEdit
GeMP and RIN have some incompatibilities with later PSP models. GeMP is incompatible with GameCategories.
Famicom (NES) / Famicom Disc System Edit
AoEX is based on NesterJ 1.12 Plus 0.61 RM, so it includes features like rewind mode, cheat codes support, rotated/mirrored screen, sepia palette, support to rare mappers (the pirate bootleg FF7 works on it), etc, but its compatibility is inferior to 1.13 beta2.
Super Famicom (SNES)Edit
SNES emulation isn't very good to begin with, but this is the fastest and most compatible emulator available right now.
Most games are unplayable, but there's a small amount of them that work really well with the right settings (Quest 64, for example).
Nintendo DS Edit
Probably the only ds emulator and is very experimental and support for it stopped a long time ago,and you can't a touch or second screen on psp properly (unless you flip the psp sideways), so it was a failure from the start.
Genesis / Sega CD Edit
Master System / Game Gear Edit
MasterBoy 2.10 (also compatible with GB and GBC)
PC Engine / CD Edit
Neo-Geo Pocket / ColorEdit
WonderSwan / Color Edit
e(mulator) v082f (multi-emulator)
Other Consoles (retro)Edit
Atari 130 / 800 / 5200Edit
Commodore Plus / 4Edit
MSX / MSX2 / MSX2+ / MSX Turbo-REdit
Sinclair ZX SpectrumEdit
TRS 80 / Tandy Color ComputerEdit