...
I don't own ANY systems on that poll!  

  (on second glance, I do own a GBC...)
I do own a few, though (though not nearly as much as djroll). 
Consoles:
Dreamcast (most often played of the consoles)
SNES
err... non-working NES?  Does that count?
Handhelds:
Nintendo Game Boy
Nintendo Game Boy Color
Sega Game Gear / SMS with adapter
Sega Nomad (the highlight of the collection)
Yes, I prefer handhelds.
I don't consider myself a dedicated gamer, though; I still mainly play them to have fun.
P.S. 
sack:  Could it be that you've missed the entire NEC console line-up?  Not to worry, though, GPengine is nearly the same thing.  No CDs, that's true, but I was considering buying a Turboexpress somewhere along the way, and the GP32 (GPengine specifically) definetely nullifies my chances of buying that handheld.