Atari: 2600, 5200, 7800, Jaguar, Lynx
Nintendo: NES, SNES, N64, GB, GBA, GBC, Famicom Disk System
Sega: Game Gear, Master System, Genesis, 32X, CD, Saturn (but only with a small ROM set) Dream Cast, Model 2, Model 3, Pico (I don't know why) Game 1000
Sony: PSP (I've found Emuparadise to be a good source although not the quickest because you have to get everything one at a time)
NEC/Turbo Grafix 16: NEC PC Engine, SuperGrafix, Turbo Grafix 16
ColecoVision
CPS3: (6 games)
Crystal System (2 games)
Neo Geo; Pocket, Pocket Color
I have emulators and ROMs for quite a few more systems that I will eventually be adding. Jason has mentioned that he wants to change how LaunchBox handles MAME and other Arcade platforms recently hopefully this can be done since I would love to add my MAME directory to LaunchBox
EDIT: Just added Virtual Boy and Turbo Graphix CD (both a small platforms)