I ended up giving away some of my older systems, so I really don't have many... I actively used my fat PS2, my DS Lite, and my PSP. I occasionally use my sister's GameCube.
Sega GameGear
Gameboy Colour
Gameboy Advance SP
Nintendo DS (Original. I don't use it enough to upgrade)
Xbox 360
PS1
PS2 (Fat and Slim. Slim being my sisters)
PSP 3000. And nope, I haven't noticed any problems with my screen.
I've got 5 that are currently in service and/or useable: PS1, PS2, PS3, DC, and PSP.
If we're including any that were previously owned and have since gone to console heaven, then my old Gakken Puck Monster handheld would bring that total up to 6.
Gameboy Color (inherited LOL), DS Lite, PS1, PS2, PSP-2000!
I'd add my inherited Gameboy mini or something (the smaller, black-and-white one running on AAA batteries), but I gave it my niece who destroyed it overnight. 8D
PS1 with travel screen- 1
PS2 Slim- 1
Nintendo Gameboy- 1
Nintendo Gameboy Pocket- 1
Nintendo Gameboy Color- 1
Nintendo Gameboy Advance- 1
Nintendo Gameboy Advance SP- 2
Nintendo DS- 1, on loan to friend.
Nintendo DS Lite- 1
Nintendo Wii- 1
Sega Dreamcast- 1
And that's just consoles which are 'mine'
Then there's my SNES, which my cousin has had for years.
I use my DS and Wii for quite a bit of my retro gaming.
Lesee...
Gameboy Pocket, Gameboy Color, Gameboy Advance, Nintendo DS Lite, Nintendo 64, Gamecube, Sega Genesis, Super Nintendo Entertainment System, PS1, PS2 (fatty, of course), PS3, X-Box (which is pretty fuggin' lame), X-Box 360 and.... I think that's it.
Wii
PS2
PS3
NGC
Sega Genesis
Super Nintendo
Dreamcast
DS
PSP
The portable ones come in handy. I'm working on modding the PSP right now though so I can steal internet with it. I've been through 3 dreamcasts now just because they keep breaking and this is my second PS2.
I like the old Genesis and Super Nintendo for games like Sonic and Mario.