I didn't get to enjoy the 8 bit era much since I was born in 85, but I played entirely too much Bomber Raid on the SEGA Master and The Legend of Zelda on the NES. I also never owned a Super NES and am a terrible person for it.
Other systems, going by what system I played said game on --
N64: GoldenEye, Mario Kart 64, Super Smash Bros, Turok 2, Ocarina of Time. Five games that I spent ENTIRELY too much time playing, especially SSB and MK64 in college.
PS1: FF7, 8, and 9. I don't care what anyone says I enjoyed the hell out of 8. I still play each of them every now and then when I get really bored and need something to play. I'm trying to think of other PS1 games I really enjoyed but coming up blank, always been more of a PC gamer than anything.
PS2: FF10. Yeah the protag is a whiny cunt and some of the characters and voice acting are laughably bad (laughably bad, see what I did there?) but it had the best combat system of any FF IMO.
PS3: Another system I didn't even own until 2011, but The Last of Us is one of those games that will easily stand the test of time. Perfection in every way except maybe the actual combat.
PS4: Nothing extremely spectacular that I've really enjoyed except for Shadow of Mordor. Complete surprise and a great game. Haven't gotten a chance to play Horizon yet, maybe during the summer when I get some extra time off work.
Xbox: Halo and Halo 2 are pretty much the only games I played, never owned the system myself. Halo put competitive console shooters on the map and Halo 2 perfected it. Despite my undying hatred for certain things it made popular like the minimap, 2 gun system, and regenerating health/shields, I can't ignore its importance.
Xbox 360: GTA5 without question. Picked it up for PS4 as well, still fire it up to fuck around every now and then.
Xboner: Eh really nothing exclusive I find spectacular
GameBoy: The original Pokemon Red/Blue, Legend of Zelda: A Link to the Past. Pokemon doesn't really hold up as well but still the inaugural entry to a big franchise.
PC: Where I've always spent the majority of my time gaming --
Command & Conquer: Tiberian Dawn (or whatever the title was for the original)
Command & Conquer: Red Alert
Sim City 2000
BioShock
BioShock Infinite
Star Wars: Knights of the Old Republic
A bunch of early~ish id software games: Doom, Doom 2, Quake, Quake 2
Borderlands 2, loved the original but the sequel did everything better
Half-Life, Half-Life 2, Counter-Strike. Started playing CS pretty early on when it was still a mod for HL1 and sunk a lot of hours into it, and HL2 was probably the first game I can remember that told a story in a way that would rival the best Hollywood has to offer.
Dragon Age: Origins
Fallout: New Vegas, would put 3 on here if Obsidian hadn't taken a giant shit all over Bethesda by doing it so much better
Homeworld, a great game that I never really got all that great at but can appreciate it for what it did
Mass Effect trilogy, I know it's hard for some people here to let shit go but I enjoyed the hell out of the whole ride until the very ending. While I was rather upset at the half assed copout way it ended up everything leading up to it was awesome.
The Witcher 3, another game that puts storytelling in the forefront and how it can make a great game
Xcom/Xcom 2
StarCraft & Diablo II, two games that took entirely too long for their (disappointing) sequels to come out. I wasted so many hours playing D2 in high school and college.
Total Annihilation. Probably my single favorite game of all time and often overlooked, was IMO the superior RTS to StarCraft in its time. The community and mods that came out for it still impress me.
World of Warcraft and EverQuest. The amount of time I spent playing these isn't measured in hours or days but in fucking years. I know my actual /played time across all my WoW characters combined is well over a year, and my EQ characters probably had quite a few months spread across them.
Battlefield franchise. Never played any prior to Battlefield 2 but I enjoyed the shit out of that and ended up playing a ton of Bad Company 2, BF3, and BF4 as a result.