The Dreamcast is the only console of it's generation (and I'm placing it in the N64/ PSX generation for the sake of this argument) that remains hooked up all the time in my game room and still gets constant use. Since I started playing NES emus on it, it's pretty much replaced my NES as well. Three systems that I always have hooked up: PS2, DC, VCS. The others just get hooked up for a few days and then put away again.
Okay, well the Vectrex is always hooked up, but since all it actually has to be connected to is power, that one doesn't really count.
-S