I almost wish it was more of a competition, but my answer is the PS1, no contest. It had an amazing, diverse library that kickstarted many fantastic series and both the visual and audio style of the console just gives me a fuzzy feeling that has not been matched. In second and third place are the PS2 and the SNES.
For handhelds it'd have to be the DS Lite. The DS library was great enough, but it's full backwards compatibility with GBA games just brought it to the next level. Loved mine until the day it died. Second and third place goes to the New 3DS XL and the Vita. Though the Vita only takes that place when it is hacked.