Recommend a game for every year since 2003

2003: Day of Defeat - There really weren't many choices for steam games back then.
2004: Half-life 2
2005: Resident Evil 4 - While I don't believe it was a steam release then, the game did originally come out that year..and it's awesome. Steam only had the HD version though.
2006 - Elder Scrolls Oblivion
2007: CoD4:Modern Warfare - Prob the one that popularized the franchise.
2008: Mass Effect.
2009: Left 4 dead 2
2010: Battlefield Bad Company 2
2011: Payday: The Heist
2012: Chivalry
2013: Rust
2014: Alien: Isolation
2015: Castaway Paradise - it's like Animal Crossing! What's not to love?!
2016: Quantum Break
2017: Conan Exiles

Good Idea. I just made a list for myself in sense of replay value, so this might be a little chaotic.

2003: SW Jedi Academy, XIII, Prince of Persia SoT, Unreal 2, Wolfenstein ET, Rainbow Six 3, Postal 2
2004: GTA:SA, SW:KOTOR2, Painkiller, Vampire the Masquerade Bloodlines, Far Cry, Doom 3, Evil Genius, HL2
2005: FEAR, Psychonauts, Still Life, Sniper Elite
2006: ArmA, Company of Heroes, Dead Rising, Flatout 2, HL2E1, Hitman BM, Neverwinter Nights 2, Prey
2007: BioShock, Crysis, HL2E2, Mass Effect, Overlord, Portal, Sam&Max S1&2, Stalker, Surpreme Commander, The Witcher
2008: Braid, Burnout Paradise, Dead Space, Edna&Harvey: The Break Out, GTA4
2009: ArmA2, Borderlands, FEAR2, Killing Floor, L4D2, Mirror's Edge, Overlord 2, PvZ, Prototype, Quake Live, Scribblenauts, The Whispered World
2010: Amnesia, BF:BC2, Alien Swarm, BioShock 2, Fallout NV, Grotesque Tactics, Mafia 2, Mass Effect 2, Metro 2033, A New Beginning, Singularity, StarCraft 2, Super Meat Boy, VVVVVV
2011: Binding of Isaac, Dead Island, Deus Ex HR, Crysis 2, Harveys new Eyes, Magicka, Minecraft, Portal 2, Red Orchestra 2, Stanley Parable, Terraria, To the Moon, Witcher 2, BF3, Limbo
2012: Borderlands 2, Deponia, Dishonored, Far Cry 3, Hotline Miami, Lucius, ME3, The Walking Dead
2013: Antichamber, ArmA3, BF4, Bioshock I., Brothers (atots), Battleblocks T., CoH2, Crysis 3, Don't Starve, FC3 Blood Dragon, Evoland, Metro LL, Night of the Rabbit, Spelunky, Shadow Warrior, Gunpoint, Rogue Legacy,
2014: BoI Rebirth, FC4, Insurgency, Shovel Knight, Vanishing of Ethan Carter, War for the Overworld, Wolf. TNO, Wasteland 2, Heavy Bullets, Valiant Hearts, UnEpic
2015: GTA5, Ori and the Blind Forest (?), Pillars of Eternaty (?), Witcher 3, Grim Fandango Remastered, Hotline Miami 2, Nuclear Throne, Party Hard
2016: Dishonored 2, Doom, Firewatch, No Mens Sky, The Witness (?), DoTT Remastered, Superhot, Enter the Gungeon, Ghost 1.0, Owlboy (?)
2017: probably Hitman...

Alien Shooter - 2003
2004 - Can't think of anything
Star Wars Battlefront II - 2005
TES IV Oblivion - 2006
Bioshock - 2007
Mass Effect - 2008
Star Wars The Force Unleashed - 2009
Beat Hazard - 2010
The Binding of Isaac - 2011
Tales of the Maj'Eyal - 2012
Bioshock Infinite - 2013
Murdered Soul Suspect - 2014
Chroma Squad - 2015
Batman Telltale Series - 2016
2017... To be seen although I suspect Mass Effect Andromeda to be taking this place

Honorable mentions for a couple of games not on Steam
FF7: Crisis Core - 2008
Kingdom Hearts Birth by Sleep - 2010
Mass Effect 3 - 2012
Dragon Age Inquisition - 2014

I also tried to avoid some of the more obvious games people were gonna mention but... well, some are just great games and should always be mentioned.

2003: Deus Ex
2004: Deus Ex
2005: Deus Ex
2006: Deus Ex
2007: Deus Ex
2008: Deus Ex
2009: Deus Ex
2010: Deus Ex
2011: Deus Ex
2012: Deus Ex
2013: Deus Ex
2014: Deus Ex
2015: Deus Ex
2016: Deus Ex
2017: Deus Ex

No one mentioned Assassin's Creed 1 or 2??? Really!!

Interesting topic , may come back to int when i wake up >.>

If i remember D:

can someone reply so i do

2003: Wolfenstein: Enemy Territory
2004: Rise of Nations: Thrones and Patriots OR Counter-Strike: Source(some would say Half-life 2 nut I didnt play that untill years later)
2005: Prince of Persia: The Two Thrones
2006: The Elder Scrolls IV: Oblivion
2007: Heroes of Might and Magic V: Tribes of the East (DLC)
2008: Fallout 3
2009: Call of Duty: Modern Warfare 2
2010: Call of Duty: Black Ops OR Fallout: New Vegas OR Civilization V
2011: The Elder Scrolls V: Skyrim
2012: Counter-Strike: Global Offensive
2013: Grand Theft Auto V
2014: Middle-earth: Shadow of Mordor
2015: The Witcher 3: Wild Hunt
2016: Battlefield 1

2003: Max Payne 2: The Fall of Max Payne
2004: Half-Life 2
2005: Grand Theft Auto: San Andreas (that year for PC)
2006: The Elder Scrolls IV: Oblivion
2007: Portal
2008: Left 4 Dead
2009: Burnout Paradise: The Ultimate Box (that year for PC)
2010: Mass Effect 2
2011: Deus Ex: Human Revolution
2012: Black Mesa (released like mod)
2013: Brothers: A Tale of Two Sons
2014: - (played only a few)
2015: - (played only a few)
2016: - (played only a few)
2017: - (played only a few)

2003 - Max Payne 2
2004 - Half-Life 2
2005 - Splinter Cell Chaos Theory
2006 - Company of Heroes
2007 - Bioshock
2008 - Mirror's Edge
2009 - Batman Arkham Asylum
2010 - Civilization 5.
2011 - Skyrim
2012 - Dishonored
2013 - GTA 5
2014 - The Wolf Among Us or Metro Redux
2015 - Witcher 3
2016 - The Flame in the Flood

2003 - Day of Defeat
2004 - Evil Genius
2005 - Knights of Honor
2006 - Company of Heroes
2007 - Team Fortress 2
2008 - Fallout 3
2009 - Saints Row 2
2010 - Sid Meier's Civilization V
2011 - The Elder Scrolls: Skyrim
2012 - Crusader Kings II
2013 - Saints Row IV
2014 - South Park: The Stick of Truth
2015 - Fallout 4
2016 - Don't Starve Together

Games that i played, finished and that I can fully recommend:

2003 Star Wars: Knights of the Old Republic, Grand Theft Auto: Vice City, Freedom Fighters
2004 Far Cry, Half-Life 2, Rome: Total War
2005 SWAT 4, Fahrenheit, Psychonauts
2006 Company of Heroes, Hitman: Blood Money, Bully: Scholarship Edition
2007 S.T.A.L.K.E.R.: Shadow of Chernobyl, The Witcher, Crysis
2008 S.T.A.L.K.E.R.: Clear Sky, King's Bounty: The Legend
2009 S.T.A.L.K.E.R.: Call of Pripyat, Assassin's Creed II, Batman: Arkham Asylum, The Saboteur
2010 Just Cause 2, Mafia II, Battlefield: Bad Company 2, Alpha Protocol: The Espionage RPG
2011 L.A. Noire, Deus Ex: Human Revolution, The Witcher 2: Assassins of Kings
2012 Far Cry 3, Dishonored, Hitman: Absolution, Risen 2: Dark Waters, Max Payne 3, XCOM: Enemy Unknown, Ghost Recon: Future Soldier
2013 Tomb Raider, Metro: Last Light, The Wolf Among Us: A Telltale Games Series
2014 Diablo III: Reaper of Souls

Chaser was released in 2003 , one of my 1st games I played , also on of the best games I played since then
https://en.wikipedia.org/wiki/Chaser_(video_game)
http://store.steampowered.com/app/39670/