I'll assume this doesn't include handheld consoles. I'll try to pick the console I actually prefer and not which one I think was most historically significant. Therefore consoles that are backwards compatible will automatically get a significant boost i.e. PS2+PS3 will beat PS1 by default.
Sega Saturn - Just an incredible selection of games, Panzer Dragoon series, Shining series, Nights, Virtua Fighter games, Dragon Force, it even has my favourite versions of Sonic 1-Knuckles in Sonic Jam. Mega Drive and Dreamcast are very close though so I'm not completely sure I can call this (this might be a running theme with the other consoles)
PS4 - I find it hard to choose between PS2, PS3 and PS4. PS1 is out since all of its games are available to play on PS2/PS3. I'll go with PS4 though, Sony's first party games are at their best in my opinion with Uncharted 4, Spider-Man, God of War, Horizon Zero Dawn and Shadow of the Colossus coming to mind. A lot of my favourite games from previous systems have been remastered for PS4 too, inlcuding many Final Fantasy games, Symphony of the Night, Secret of Mana, Shenmue 1&2, Uncharted 1-3, The Last of US, Kingdom Hearts games, Star Ocean games, several PS2 classics and a whole load of classic game collections. Then there are plenty of new 3rd party titles like Sonic Mania and Forces, Yooka Laylee, Bloodstained, Yakuza games, No Man's Sky, a ton of JRPGs and countless other good titles. I think I might own more games for PS4 than any other system. But probably the real tiebreaker is VR. It requires a peripheral but VR has greatly enhanced some existing games as well as introducing new ones, Wipeout, Tetris Effect and Astrobot really stand out to me.
Wii U and Switch (tied) - Wii U offers all Wii games and a ton of Virtual Console games that include some of my favourite games ever from NES, SNES and N64 (controls are off on N64 though). It also allows me to play some of my favourite Gamecube games like Windwaker, Twilight Princess, Metroid Prime Trilogy and Pikmin (through Wii mode). As well as some good Wii U titles like Mario 3D World, Xenoblade Chronicles X, Pikmin 3 and Yoshi. Meanwhile Switch offers upgraded ports of many key Wii U titles, some new games like Mario Odyssey, Xenoblade 2, Smash Bros Ultimate, Yoshi and Kirby. It also has many of the same Final Fantasy games as the PS4 and many of the third party titles on PS4 too. I feel like the Switch will end up winning this one as some of the older games from SNES, N64, Gamecube start showing up. The Switch also doubles as a handheld so that is a bonus in my opinion.
Xbox One, I guess - I don't actually own an Xbox One but it shares a lot of multiplatform games with PS4 and also offers quite a large number of Xbox 360 games and even some original Xbox ones like Panzer Dragoon. As for exclusives, I'm not too interested but I guess if I owned the console I might like a few. I think if I owned one, it would be my Xbox of choice more often than not. If I have to choose a console that I own, then Xbox 360 hands down.
I'm a bit surprised that I tended to go for modern consoles when I think the majority of my favourite games were released in the sixth gen or earlier, but backwards compatibility, remasters and remakes can really help newer consoles. Another thing that helps modern consoles is they generally have plenty of additional features that I like and the ability to store games digitally for convinience. I also enjoy using PS Now and would probably use Game Pass if I owned an Xbox One.