Like I said, it was really hard to make this list lol. LoD came out in 2000, and much as I love the game, I can't put it over Deus Ex.

1985: Super Mario Bros.
1991: Super Mario Bros. 3 (released in Europe in 1991)
1993: Super Mario All Stars
1995: Battle Arena Toshinden
1996: Super Mario 64.
1997: Tomb Raider II
1999: Pokémon Blue
2000: Pokemon Stadium
2001: GTA III
2002: GTA Vice City
2004: GTA San Andreas
2005: Star Wars Battlefront II
2006: Super Mario Galaxy
2008: Star Wars The Force Unleashed
2009: Prototype
2010: God Of War III
2013: GTA V
2014: Bayonetta II
2016: Uncharted 4
2017: Super Mario Odyssey
2018: God Of War

1989: Indiana Jones and the Last Crusade
1990: The Secret of Monkey Island
1991: Monkey Island 2: LeChuck’s Revenge
1992: Pinball Dreams
1993: Day of the Tentacle (close second: Return to Zork)
1994: UFO: Enemy Unknown (One Must Fall: 2097 and Jagged Alliance are contenders)
1995: Descent (close second: Star Wars: Dark Forces)
1996: Duke Nukem 3D (close second: Resident Evil)
1997: ???
1998: Baldur’s Gate (StarCraft is close second)
1999: Heroes of Might & Magic 3
2000: Baldur’s Gate 2 (close second: The Legend of Zelda: Majora’s Mask)
2001: Wizardry: Tale of the Forsaken Land (close second: Pikmin)
2002: Resident Evil Zero
2003: Beyond Good & Evil
2004: Resident Evil 4
2005: ???
2006: Okami (close second: The Legend of Zelda: Twilight Princess)
2007: Etrian Odyssey (contenders: Fire Emblem: Radiant Dawn and Hotel Dusk: Room 215)
2008: Mario Kart Wii
2009: Demon’s Souls (contenders: Monster Hunter Tri and Little King's Story)
2010: Xenoblade Chronicles
2011: Pandora's Tower (close second: Deus Ex: Human Revolution)
2012: Fire Emblem Awakening (contenders: Etrian Odyssey IV: Legends of the Titan and Kid Icarus: Uprising)
2013: Etrian Odyssey Untold: The Millennium Girl
2014: Hyrule Warriors (contenders: Mario Kart 8 and Persona Q: Shadow of the Labyrinth)
2015: Tokyo Mirage Sessions ♯FE (close second: Pillars of Eternity)
2016: Etrian Odyssey V: Beyond the Myth
2017: The Legend of Zelda: Breath of the Wild

I was born in 1989 but I started playing on the NES when the SNES was out.
So I skipped SNES to jump directly from NES to N64.
 
That’s why there are NES games in the SNES Years :)
(Runner Up in brackets)
 
NES ERA:
1994 – Super Mario Bros 3 (Super Mario Bros)
1995 – Mega Man 2 ( Tetris )

N64 ERA:
1997 – Mario Kart 64 (Goldeneye 007)
1998 – Pokemon Red (Super Mario Land 2)
1996 – Super Mario 64 ( - )
1999 – Zelda Ocarina of Time (Pokemon red)
2000 – Banjo-Kazooie ( Yoshi’s Story )

GC ERA:
2001 – Luigi’s Mansion (Star Wars: Rogue Squadron II)
2002 – Super Mario Sunshine ( Sonic Adventure II Battle)
2003 – Mario Kart: Double Dash (Super smash Bros. Melee)
2004 – Zelda: The Wind Waker (Metroid Prime)
2005 – Tales Of Symphonia (Metroid prime 2 :Echoes)
 
WII ERA
2006 – Zelda Twilight Princess ( XIII on GC)
2007 – Super Mario Galaxy (Metroid Prime 3: Corruption)
2008 – Mario Kart Wii (Super Smash Bros. Brawl)
2009 – Okami (Super Paper Mario)
2010 – Donkey Kong Country Returns (Red Steel II)
2011 – Zelda: Skyward Sword ( - )
 
Wii U ERA / PC 
2012 – Far Cry 3 (Darksiders)
2013 – Tomb Raider (Batman Arkham Asylum)
2014 – Batman Arkham City (Super Mario 3D World)
2015 – Mario Kart 8 (Zelda The Wind Waker HD)
2016 – Batman Arkham City (Darksiders II)

SWITCH ERA
2017 – Zelda: Breath of the Wild (Super Mario Odyssey)
2018 – Xenoblade Chronicles 2 ( - )
 
Honorable mention for Soul Calibur II, Rayman Legends, No More Heroes, Golden Sun, Zelda: Spirit Tracks, 1080°: Snowboarding, Diddy Kong Racing, Star Fox Adventure, Super Mario Galaxy 2.

A couple games I've never even heard of. I must now go to YouTube!

1996: Pokemon Red/Blue
1999: Motocross Madness 2
2001: Halo Combat Evolved
2002: GTA Vice City
2003: NFS Underground
2005: GTA San Andreas
2006: GTA Vice City Stories
2007: God of War 2
2008: God of War Chains of Olympus
2009: Demon's Souls
2010: God of War 3/Red Dead Redemption
2011: Dark Souls
2012: Assassin's Creed 3
2013: Gran Turismo 6
2014: Infamous Second Son
2015: Bloodborne
2016: Dark Souls 3
2017: Nier Automata

Thanks for contributing, everyone! That so many of you decided to go above and beyond my request in the OP by including runners-up has inspired me to do a follow-up list of my own second choices! So here they are...

JC's Runners-Up List

1987: The Great Giana Sisters
1988: Hidden Agenda
1989: Golden Axe
1990: Balloon Kid
1991: ToeJam & Earl
1992: Dragon Warrior IV*
1993: Day of the Tentacle
1994: Final Fantasy VI**
1995: Solar Eclipse
1996: Tomb Raider
1997: Tomb Raider II
1998: Nancy Drew: Secrets Can Kill
1999: Urban Chaos
2000: Perfect Dark
2001: Luigi's Mansion
2002: Nancy Drew: Ghost Dogs of Moon Lake
2003: Primal
2004: Baten Kaitos: Eternal Wings and the Lost Ocean
2005: Harvest Moon: Another Wonderful Life
2006: Rule of Rose
2007: Peace Maker
2008: Shin Megami Tensei: Persona 4
2009: Muramasa: The Demon Blade
2010: Final Fantasy XIII
2011: Sword & Sworcery EP
2012: Thomas Was Alone
2013: The Stanley Parable
2014: Never Alone
2015: Ori and the Blind Forest
2016: Ittle Dew 2
2017: Night in the Woods
2018 (so far): Iconoclasts

*This game is known as Dragon Quest IV in its native Japan.
**In a break with my pattern, I chose this title instead of the American one from the time for the sake of clarity.

Bonus: JC's Favorite Multi-Year Releases

1. Kentucky Route Zero
2. The Legend of Heroes: Trails in the Sky

1978: Space Invaders
1979: Bee Wary
1980: Pac-Man
1981: Donkey Kong
1982: Joust
1983: Mario Bros
1984: Boulder Dash
1985: Super Mario Bros
1986: Starflight
1987: The Legend of Zelda
1988: Zelda II
1989: Super Mario Land
1990: Super Mario Bros 3
1991: Final Fantasy IV
1992: The Legend of Zelda: A Link to the Past
1993: The Legend of Zelda: Link's Awakening
1994: Super Metroid
1995: Chrono Trigger
1996: Super Mario 64
1997: Final Fantasy VII (favorite game of all time)
1998: The Legend of Zelda: Ocarina of Time
1999: Lunar: Silver Star Story Complete
2000: Final Fantasy IX
2001: Final Fantasy X
2002: Metroid Prime
2003: The Legend of Zelda: The Wind Waker
2004: Tales of Symphonia
2005: Dragon Quest VIII
2006: The Legend of Zelda: Twilight Princes
2007: Virtua Fighter 5 Online
2008: Valkyria Chronicles
2009: Demon's Souls
2010: Fallout New Vegas
2011: The Legend of Zelda: Skyward Sword
2012: Xenoblade Chronicles
2013: Ni no Kuni
2014: Bayonetta 2
2015: Super Mario Maker
2016: Final Fantasy XV
2017: The Legend of Zelda: Breath of the Wild

I have played a lot of games, but I have missed a bunch as well, so these favorites are of course based on games I actually played and not some Metacritic score.

1991 - Super Mario World (North American SNES Release)
1992 - Street Fighter II Turbo (Worldwide Arcade Release)
1993 - Doom
1994 - Donkey Kong Country
1995 - Donkey Kong Country 2 : Diddy's Kong Quest
1996 - Tekken 2 (North American PS Release)
1997 - Mario Kart 64 (North American N64 Release)
1998 - Tekken 3 (North American PS Release)
1999 - Ape Escape
2000 - Final Fantasy IX
2001 - Ico
2002 - Metroid Prime
2003 - Silent Hill 3
2004 - Final Fantasy XI (North American PS2 Release)
2005 - Shadow of the Colossus
2006 - Final Fantasy XII
2007 - Halo 3
2008 - Metal Gear Solid 4 : Guns of the Patriots
2009 - Call of Duty : Modern Warfare 2
2010 - Amnesia : The Dark Descent
2011 - Portal 2
2012 - Journey
2013 - The Last of Us
2014 - Final Fantasy XIV : A Realm Reborn (North American PS4 Release)
2015 - Bloodborne
2018 - Shadow of the Colossus (Remake)

Some years were much more difficult than others to choose a favorite. The missing years of 2016 and 2017 were squarely devoted to FFXIV and Bloodborne if I was playing a video game at all. I don't even think I played a new release from those two years, much less had a favorite. I was mostly devoted to work, so I put gaming on the wayside. Though I have since bought Gran Turismo Sport (a 2017 game).

2001: Pokemon: Gold & Silver
2002: The Legend of Zelda: Wind Waker
2003: Pokemon: Ruby & Saphirre
2004: Ratchet & Clank: Up your Arsenal
2005: Resident Evil 4
2006: Kingdom Hearts 2
2007: Pokemon: Diamond & Pearl
2008: Super Smash Bros. Brawl
2009: Uncharted 2
2010: Red Dead Redemption
2011: Batman Arkham City
2012: Borderlands 2
2013: Pokemon: X/Y
2014: Mario Kart 8
2015: Bloodborne
2016: Pokemon: Sun & Moon
2017: The Legend of Zelda: Breath of the Wild