Egads, to dig into memories. Ok, if you insist (and Handhelds):
Atari 2600
Atari Lynx
Atari Jaguar
Atari 400 and Atari 800 XL (I used the computers as game machines so they count)
Commodore 64 (I used it as a game machine, so it counts. No longer have it)
Amiga 500 (got at garage sale for free, but didn't work)
Intellivision
Odyssey II
Vectrex
3DO
NGage
NeoGeo Pocket Color
Sega Master System (it died and I got a Power Base Convertor for Genesis)
Sega Genesis
Sega Nomad
Sega CD (Maybe my brother had it. I think I ended up with it though)
Sega Saturn
Sega Dreamcast
TurboGrafx-16
Turbo Express (portable TurboGrafx)
NES
SNES
N64
Gamecube
Wii
Gameboy, Gameboy Color, Gameboy Advance, Nintendo DS fat and thin
XBox (it died on me)
XBox 360
Playstation (still have it with the official portable screen)
PS2
PS3
PSP (original and one with video output. Yes I have two of them)
Passed on Gamegear. Decided I didn't want a portable Master System.
Not sure if I am missing something here. I feel like I might be. I did rent a NeoGeo at one time. Yes a store rented it out. It was fun doing Superspy and Cyberlip on it.
Oh, does one count emulators? I have a bunch of retro game system packs. I also tried a bunch of MAME. And I have some old stand alone portables.