I'll get things started. On the console side, I own a Dreamcast, a GameCube, a PS2 (along with quite a few PS1 games) and a Wii, while on the handheld side I own a DS and a GameBoy Advance.
I imagine my next purchase will be a PS3. After that, I'll probably get a DSi or a PSP. I'd love to get an Xbox 360, too, but I don't think that's going to happen for some time.
Anyway, enough about me--which systems do you own and play?