As of 2017, easily, Xbox 360. At least in my opinion.
It has everything, including tons of ports and revivals from earlier systems, all the way from NES to Dreamcast. Think about how long that generation was. Tons of ports of arcade games (REAL arcade games, not "Xbox Live Arcade"), HD remakes, original franchises, the births of so many popular IPs, RPGs, fighting games, Japanese shmups, indie games (including the thousands of XBLIG). There's Rock Band and other music and accessory games too. You will never have time to play all of it.
All of this on one of the most comfortable, well-designed controllers ever made. Well, except for that awful D-pad. But that's why there are so many great arcade joysticks available for it.
Runners up:
I want to say Dreamcast, because the games are so great, but 360 just has way more.
Xbox One has the backwards compatibility, yes, but they've already said that accessory games will never work, and I'm not sure that a lot of the great Japanese games will ever make it over.
NES and Super NES are timeless. But still, 360 just has way more of everything.