The first system that came to mind is the NES. I rarely played my NES when I had it, so little that I actually sold my NES consoles and about 85% of all my games for it. I would like to buy one again, but it would have to be super cheap, same with the games I let go of.
As far as consoles I've never played, I've never once played a 3DO, CDi, or Jaguar.