I agree with some of the games you chose. My list would be something like this (I'm going by European release dates).

2000: Grandia
2001: Final Fantasy IX
2002: Final Fantasy X
2003: Soul Calibur II
2004: Tales of Symphonia
2005: Metal Gear Solid 3: Snake Eater
2006: Shadow of the Colossus
2007: Okami
2008: Valkyria Chronicles
2009: Uncharted 2: Among Thieves
2010: Enslaved: Odyssey to the West
2011: Dark Souls
2012: Journey
2013: The Last of Us
2014: The Legend of Heroes: Trails in the Sky
2015: Bloodborne
2016: Dark Souls III

Lets see:

2000: Deus Ex

2001: Max Payne

2002: Mafia

2003: Max Payne 2

2006: Hitman Blood Money

2009: Batman Arkham Asylum

2010: Fallout New Vegas

das it for me

2000: Final Fantasy IX
2001: Metal Gear Solid 2
2002: Can't think of anything that stood out to me...
2003: Prince of Persia: Sands of Time
2004: Metal Gear Solid 3
2005: Shadow of the Colossus
2006: Final Fantasy XII
2007: Bioshock
2008: Metal Gear Solid 4
2009: Uncharted 2
2010: Red Dead Redemption
2011: Batman: Arkham City
2012: Journey
2013: The Last of Us
2014: Boooo but if I had a gun to my head, Dark Souls II.
2015: Bloodborne by a sliver over Witcher 3, sorry had to mention both.
2016: Uncharted 4
2017: Horizon Zero Dawn

Where do I click for 0%?

the 100% is 66% zeros. That would be your closest bet.

2000: Final Fantasy IX
Honorable mentions: Majora's Mask, Lunar: Eternal Blue Complete, Valkyrie Profile

2001: Final Fantasy X
Honorable Mentions: Devil May Cry, SSB Melee

2002: Metroid Prime
Honorable Mentions: Virtua Fighter 4, Kingdom Hearts, GTA Vice City

2003: Wind Waker
Honorable Mentions: Skies of Arcadia Legends, Soulcalibur 2 (GC), Final Fantasy X-2, FF Tactics Advance

2004: Tales of Symphonia
Honorable Mentions: Metroid Prime 2, Harvest Moon: AWL

2005; Dragon Quest VIII
Honorable Mentions: Resident Evil 4, Fire Emblem: Path of Radiance, Minish Cap

2006: Twilight Princess
Honorable Mentions: Final Fantasy XII, Okami, Mario Kart DS, Gears of War

2007: Virtua Fighter 5 Online
Honorable Mentions: Rogue Galaxy, Fire Emblem: Radiant Dawn, Blue Dragon, Pokémon Diamond/Pearl

2008: Valkyrie Chronicles
Honorable Mentions: Fallout 3, Tales of Vesperia, Lost Odyssey

2009: Demon's Souls
Honorable Mentions: Dragon Quest V

2010: Fallout: New Vegas
Honorable Mentions: Sakura Wars: SLML, Valkyria Chronicles Ii, Yakuza 3, Spirit Tracks, Bayonetta

2011: Skyward Sword
Honorable Mentions: Dragon Quest VI, Mortal Kombat, Catherine

2012: Xenoblade Chronicles
Honorable Mentions: Tales of Graces f, Lollipop Chainsaw, Virtua Fighter 5 Final Showdown

2013; Ni no Kuni
Honorable Mentions: A Link Between Worlds, Talrs of Xillia, Dragon's Crown

2014: Bayonetta 2
Honorable Mentions: Mario Kart 8 , Tales of Xillia 2

2015: Super Mario Maker
Honorable Mentions: Dragon Quest Heroes, FF Type-0, Fallout 4, Trails of Cold Steel

2016; Final Fantasy XV
Honorable Mentions: Tokyo Mirage Sessions #FE, Odin Sphere Leifthrasir, Nights of Azure, 7th Dragon III

2017: Breath of the Wild
Honorable Mentions: Super Mario Odyssey, Persona 5, Xenoblade Chronicles 2, NieR: Automata

The century started in 2001, so starting there.

2001 - Star Wars Rogue Squadron 2 Rogue Leader

2002 - Metroid Prime

2003 - Tie between Star Wars KOTOR and Legend of Zelda the Wind Waker

2004 - Half Life 2

2005 - Resident Evil 4

2006 - Legend of Zelda Twilight Princess

2007 - Super Mario Galaxy

2008 - Fallout 3

2009 - Batman Arkham Asylum

2010 - Super Mario Galaxy 2

2011 - Legend of Zelda Skyward Sword

2012 - Mass Effect 3

2013 - Fire Emblem Awakening

2014 - Super Smash Bros. 4

2015 - Witcher 3

2016 - Overwatch

2017 - Legend of Zelda Breath of the Wild

2000: Command & Conquer: Red Alert 2
2001: Pokémon Gold and Silver/Advance Wars
2002: Kingdom Hearts
2003: Star Wars: Knights of the Old Republic (makes the TLJ look like poop)
2004: Fable
2005: Soulcalibur III
2006: The Elder Scrolls IV: Oblivion/Resistance: Fall of Man
2007: Super Mario Galaxy/Halo 3/ Cod 4
2008: Fallout 3/Fable 2/Sw force unleashed/ castle crashers/GTA IV/SC IV/ Smash bros brawl... too many to list.
2009: Borderlands
2010: Red Dead Redemption
2011: Batman Arkham City
2012: Borderlands 2
2013: Injustice: Gods Among Us
2014: Shovel Knight
2015: LIFE IS STRANGE
2016: Ratchet & Clank reboot
2017: Zelda BOTW/ Life is strange 2

2000: Final Fantasy IX
2001: Metal Gear Solid 2: Sons of Liberty
2002: Metroid Prime
2003: The Legend of Zelda: The Wind Waker
2004: Half Life 2
2005: Civilization IV
2006: Metal Gear Solid 3: Subsistence
2007: Team Fortress 2
2008: Shin Megami Tensei: Persona 4
2009: Mario & Luigi: Bowser's Inside Story
2010: Super Mario Galaxy 2
2011: Dark Souls
2012: Xenoblade Chronicles
2013: Europa Universalis IV
2014: Super Smash Bros. 4
2015: Metal Gear Solid V: The Phantom Pain
2016: Dark Souls III
2017: Yakuza 0/Persona 5/The Legend of Zelda: Breath of the Wild

2000-Zelda: Majora's Mask
Still the best plot in Zelda and a game that uses its gameplay to tell a story about death and human connections, definitively not what you'd expect from Nintendo.

2001-Silent Hill 2
The most well written game I've ever played, by a long shot. James' plight still haunts me like no other game ever has.

2002-Metroid Prime
Fantastic combat, puzzle solving and world exploration coupled with intriguing lore told through collectables, which feels right at home in a metroid game, leaving the amount of plot in the game up to players to decide.

2003-Prince of Persia: Sands of Time
Likeable characters, excellent platforming and gameplay in sync plot in an elegant manner (both are about correcting mistakes)

2004-Tales of Symphonia
havent played it in a long time, but i remember really enjoying it and there's not much else this year I played more. I guess Metroid Prime 2 would be the closest runner up

2005-Shadow of the Colossus
My favorite game by my favorite developer. Absolutely amazing concept, flawlessly executed (except for framerate) coupled with intriguing world, themes and ideas.

2006-Okami
A little slow to get started, but really endearing story and refined the zelda gameplay with deeper combat and excellent bosses. The build up to Orochi and Ninetails were definitively highlights.

2007-Super Mario Galaxy
Just behind 64 (and maybe Odyssey) for my favorite Mario game. I miss the exploration, but the excellent level desgin and controls more than made up for it.

2008-Braid
A more "artistic" explorarion of I was talking about with PoP sands of time. Amazing puzzles push the concept as far as it will go, making for an excellently desgined game.

2009-Demon's Souls
Still has the best selection of bosses in the souls series if you ask me. Not to mention it was the first to come up with the excellent combat system and cryptic lore

2010-Donkey Kong Country Returns
not many a lot of games I liked this year, but dkcr is pretty good regardless

2011-Dark Souls
Took the already pretty strong foundation of demons souls and placed it in a metroidvania-esque world, allowing for interesting sequence breaks and more explorarions

2012-Journey
Great game feel and visuals come together to create a game that manages to elevate itself above other 'walking simulators' by tackling themes of rebirth and relationships purely through gameplay

2013-Zelda: A Link Between Worlds
TLoU came really close, but in the end ALbW is just better designed imo. Maybe it's me being a hipster, but this is genuinely one of my favourite zelda games

2014-Donkey Kong Tropical Freeze
Possibly my favorite 2d platformer, I love how high the skill ceiling is. Just look for some speedruns of this game and you'll know what i mean

2015-Bloodborne
Everything ds2 and ds3 should've been, with a new setting and new mechanics. This is probably my favorite souls game in terms of plot and lore.

2016-The Last Guardian
Stupid bottom prompts aside, I really loved this game. I understand its not for everyone, since some of its design decisions would make for a bad game everywhere else, but everything here is geared towards creating a real relationship to explore themes of nature vs programming, which I loved and cant wait to replay to learn more about how it works

2017-Zelda: Breath of the Wild
Easily the best open-world exploration anywhere. Just the act of moving from point A to B is fun and the freedom to experiment with combat keeps things really engaging.