NES Gen - Zelda, Mario, Mario 3, Castlevania, Hogan's Alley (played the shit out of that when I was little)
SNES Gen - Final Fantasy VI, Chrono Trigger, F-Zero, Street Fighter 2 Turbo, Mortal Kombat 2.
PS1 Gen - Mario 64, FFVII, Goldeneye, Mario Kart 64, Metal Gear Solid. Lot of other ones that come really close like Resent Evil, Silent Hill, Gran Turismo, so on.
PS2 Gen - GTA3, Silent Hill 2, Resent Evil 4, Half Life 2, FFX
X360 Gen - Bioshock, Mass Effect 1, 2 and 3, Skyrim, Batman: Arkham City, Last of Us. Lot of honorable Mentions - Gear of War, Halo 3, Uncharted 2, Red Dead Redemption, GTA 4 and 5, Modern Warfare, Killzone 2, Dishonored, Sleeping Dogs. Honestly probably my favorite generation of all time, only rivaled by the PS1 days.
Current Gen - Witcher 3, Horizon Zero Dawn, Breath of the Wild, Bloodborne, Resident Evil 7.
this generation: Witcher 3, XCOM 2, Alien Isolation, Horizons, Super Mario Maker
360/PS3: Last of Us, GTAV, Mass Effect series, Red Dead Redemption, Fallout 3
PS2/Xbox/GC: RE4, Half Life 2, FEAR, KOTAR, Company of Heroes (tail end of this generatio but released prior to PS3)
After that...no idea. Just Half Life! Oh the best MP game of all time TFC and TF2.
First and second gen home consoles are a little before my time. I remember playing the Atari 2600 as a little boy, but not enough to truly have any favorite or reliable memories. Pac-Man and Pitfall were among my most played.
Third gen: The NES is THE only console I owned and I played like an addict.
-Super Mario Bros.
-The Legend of Zelda
-Super Mario Bros. 3
Fourth gen: I owned the SNES and the Genesis.
-The Legend of Zelda: A Link to the Past
-Final Fantasy III
-Sonic the Hedgehog 2
Fifth gen: I owned the PlayStation and the N64.
-Super Mario 64
-The Legend of Zelda: Ocarina of Time
-The Legend of Zelda: Majora's Mask
-Resident Evil 2
Sixth gen: I owned the PS2 and the GameCube.
-Eternal Darkness: Sanity's Requiem
-Resident Evil 4
-The Legend of Zelda: Twilight Princess
-Grand Theft Auto III
Seventh gen: I owned the PS3 and the Wii.
-Super Mario Galaxy
-Call of Duty 4: Modern Warfare
-The Last of Us
-Batman: Akrham City
Eighth gen: I own the PS4, Xbox One S, and the Wii U.
-Grand Theft Auto V
-The Legend of Zelda: Breath of the Wild
-Batman: Arkham Knight
-Mario Kart 8
Don't know how best to do this other than by machine I own or have owned.
Amiga 600: Mortal Kombat 2, Street Fighter 2, Syndicate, Sensible World of Soccer, Dune II
PS1: Resident Evil 2, Metal Gear Solid, Pro Evolution Soccer, Final Fantasy VII, Final Fantasy VIII
PS2: Onimusha 2, Metal Gear Solid 3, Grand Theft Auto: Vice City, Pro Evolution Soccer 5, Star Wars Battlefront 2
I've been a PC guy since before the PS3 came out, so I'm somewhat across eras on this, so to keep it brief:
Warhammer 40K: Dawn of War (all bar 3, because it looks shit)
Star Trek: Starfleet Command 3
Star Trek: Bridge Commander
Dragon Age Origins & 2
Mass Effect 1 & 2
Batman: Arkham Asylum & City
Hitman 2017 & Absolution
Final Fantasy XIV
Grand Theft Auto IV & V
Splinter Cell (Blacklist but also Conviction)