It's usually considered to not be a console, but since it's my primary gaming system I'm going to say PC. Not only does it have the best possible graphics of all gaming systems, but games are typically cheaper for it via Steam, it has a good number of indie games and gems such as M&B:W and RTS's and you can either use mouse+keyboard or use a controller if you want to.
Strictly speaking in terms of consoles though, I'm going to have to say the 3DS if only because of Nintendo's IPs and Monster Hunter. Haven't really played any other recent generation consoles besides the PSP to be able to comment on, and the PSP didn't really have a tremendous amount of games which were really worth playing besides Monster Hunter and the Phantasy Star Portable games and a few others.
Xbox 360, that's what I used to play most of my favorite games. I bought an Xbox One but the choice of games is still REALLY small and I wish I could play my 360 games on there.
I basically only play on my PC now for gaming (and my 3DS but that is not really the same thing), so I'd have to say N64 and GameCube for nostalgia reasons. I played some great games on those consoles growing up.
Gamecube and N64 have the most of my favorite games of all time on them, I'd have to really think about it to choose between them but it might be N64 (although GC has the vastly superior controller). Although I am deeply in love with my 3ds xl too of course.
For me, the Super Nintendo Entertainment System easily takes the cake. Its undeniably awesome and well-rounded game library made the console a joy to play. Most of the quality games are aging so well that they effortlessly stand the test of time.
Want to play some Japanese games? No need to import the Super Famicom system even though it's much nicer to look at it than the blocky American SNES design. With a very simple physical modding or by owning certain clone consoles, you'll be going for extra miles as you could get your Super Famicom games to work on your system. There are some of them don't require learning much Japanese in order to play.
For me, the Super Nintendo Entertainment System easily takes the cake. Its undeniably awesome and well-rounded game library made the console a joy to play. Most of the quality games are aging so well that they effortlessly stand the test of time.
Poratable - DS Lite, since it can play some of my favorite games of all time.
Home - GameCube. I don't really play any console games, but when I was younger I used to play Kirby Air Ride and Super Smash Bros Melee with my brother all the time. Good memories.