Mine's the PSP, never have I spent so much time on any game system, I haven't touched my PS3 or my brother's PS4 in over a month because I've been playing my vita games or watching youtube videos.
Got my first PSP when the first Dissidia came out, and started becoming a serious gamer, we also got a PS3, but I didn't really feel like playing it, despite getting the awesome game "Chronicles of Riddick: Assault on Dark Athena". All I would play was Dissidia, I started to master it, I was able to beat the game without ever even attempting a dodge or block, and nearly beat Inner Chaos doing so. Then I got a plethora of awesome games, but being 12 back in 2009, I couldn't really get all the games I wanted. I do however, today, have most of the games I was craving to get back then.
If anything, I have always been more of a portable gamer.
The NDS was pretty great too, but didn't appeal to me that much, I have fond memories of playing Phantom Hourglass but from what I've seen, I never came close to beating it. I beat the Ghost Ship and got back Tetra, but thats about it.
The PS2 was a great console, and probably the one I spent the most time on overall. Consoles have since been 'better', but the PS2 was a perfect bridging console that showed where console video gaming could go. Also, just generally a great selection of games for it.
Pretty much for the same reason everyone is adding the SNES to the list. It had a nice balance between how much effort was put into gameplay and how much delved into graphics. Great selection of games, playable on the go, backlit and compatible with the GBA if you really need to play it on your TV. Backwards compatible with an great library of games.
Not to mention the great ratio on quality vs price.
N64 was my first introduction into gaming. Classic stuff.
PS2 is a bit of a crossroads for me. When it worked it was probably the most fun with the massive quantity of games but I went through 3 of them and had major issues with arguably its best game(San Andreas).
Haven't had any issues with the PS3/PS4 but haven't played that many games on either so......