No particular order and for PC only, excluded a few games since they haven't aged well, or because no one plays it any more in multiplayer.
Adventure:
Curse of Monkey Island
Grim Fandango
Gabriel Knight 2: The Beast Within
Broken Sword: Shadow of the Templars
Broken Sword 2: The Smoking Mirror
Broken Sword 5: The Serpent's Curse
The Wolf Among us
Action-Adventure:
Batman: Arkham Asylum
Batman: Arkham City
Deus Ex: Human Revolution
Middle-Earth: Shadow of Mordor
Saints Row: The Third
Sleeping Dogs
Grand Theft Auto: San Andreas
Platform:
Child of Light
Dust: An Elysian Tail
Mark of the Ninja
Lara Croft, and the Guardian of Light
Roleplaying Games:
Baldur's Gate
Dragon Age: Origins
The Elder Scrolls V: Skyrim
Fallout
Fallout 2
Fallout: New Vegas
Mass Effect
Mass Effect 2
Mass Effect 3
South Park: The Stick of Truth
Diablo
Diablo 2
Diablo 3
The Witcher 2: Assassins of Kings
The Witcher 3:: The Wild Hunt
Valkyria Chronicles
Ys: Origins
Divinity: Original Sin.
Pillars of Eternity
Casual:
Dwarfs!?
Faerie Solitaire
FTL: Faster than Light
HuniePop
Plants vs. Zombies
Papers, Please
Hotline: Miami
Worms 2
Shooters:
Alien vs. Predator
Counter Strike: Global Offensive
Call of Juarez: Gunslinger
Duke Nukem 3D
Far Cry 3
Half-Life
Half-Life 2
Left 4 Dead 2
Shadow Warrior
Shadow Warrior (2013)
Wolfenstein: The New Order
Warhammer 40,000: Space Marine
Metro: The Last Light
Strategy:
Dungeon Keeper
Theme Hospital
Heroes of Might and Magic 3
Warcraft 3
Command & Conquer: Red Alert
Command & Conquer: Red Alert 2
Starcraft
Starcraft 2
Warhammer 40,000: Dawn of War
Warhammer 40,000: Dawn of War - Dark Crusade
Warhammer 40,000: Dawn of War 2 - Retribution
Warhammer: Shadow of the Horned Rat
XCOM: Enemy Unknown
Total War: Shogun
Total War: Shogun 2
This list is great. You are a fellow after my own heart, Sir.
I'd like to add to it though.
Adventure Games
Monkey Island 1-2
King's Quest (it started the whole genre)
Loom
Day of the Tentacle
Action Adventure
Jedi Knight 1-3
Platform Games
Ducktales
Commander Keen 1-6
RPGS
Might and Magic 6-8
Ultima 5-7
Betrayal at Krondor
Morrowind
Planescape:Torment
Knights of the Old Republic 1-2
Shooters
Wolfenstein 3D
Doom
Dark Forces
We have great tastes in video games. Now I declare that we are the 3 brothers: Ridwan, Rawgrim and KAvlad
My alternative games to some of the above games plus some other games:
Doom II (better than the original)
Heroes of Might and Magic 4 (some good innovations)
Heroes of Might and Magic 5 (best Heroes game to date)
Monkey Island 1, 3 and 5
Total War: Medieval II
Worms: World Party
Assassin's Creed 1,2 and 4
Prince of Persia: WW (2004)
Prince of Persia (2008)
Civilization III: Conquests
Civilization V: BNW
Endless Legend
Age of Empires II: Conquerors
Sid Meier's Colonization (1994)
American Conquest: Fight Back
Dragon Ball Xenoverse
BioShock series (just for being in the library!)
Victoria I: Revolutions, Victoria II: A House Divided, Crusader Kings II (with Rajas of India DLC), Europa Universalis IV (with random America DLC)
Borderlands 2
Call of Duty 2, World at War and Black Ops 2
Dark Souls 2
Divinity - Original Sin
Galactic Civilizations III and GC II: Twilight of Arnor
GTA 1, 2, San Andreas, The Lost and Damned, GTA V
Kings Bounty Legend and Armored Princess
Neverwinter Nights Diamond Edition and NWN 2: MotB
Jade Empire
Mass Effect 1 and 2
Revolt
Micro Machines 3 and 4
SimCity 2000 and SC 4 Rush Hour
Unreal, Unreal Tournament, UT 2004 and UT III (the first and the last suffices though)
Toy Story 2!
Tribal Rage (bashed strategy game with many awesome elements!)
Probably some more.