Ok, here is a decent list of video game genres,
based off wikipedia:
I've underlined the ones that are dying or defunct these days.
Action:
Action Adventure: Ocarina of Time, Tomb Raider
Action Roleplaying: Diablo 2, Skyrim
Adventure: Grim Fandango, Gabriel Knight
Beat-em Up: Double Dragon, Streets of Rage, TMNT, Dungeons and Dragons: Shadow of Mystara
Fighting: Street Fighter, King of Fighters, Injustice, Soulcalibur
FPS: Doom, CS
Kart Racing: Super Mario Kart
Maze: Pac- Man, Bomberman I suppose, Gauntlet?
MMO: World of Warcraft
Platform: Mario, Sonic
Platform Adventure: Metroid-vanias, probably the Mega Mans, Cadash
Puzzle: Tetris
Puzzle Platformer: Portal (no clue, but maybe like Bubble Bobble, City Connection or Joust?)
Racing: Outrun
RTS: Starcraft, Red Alert
RPG/ JRPG: Pokemon Silver, Final Fantasy VII
Role-playing shooter: Fallout 3
Run and Gun: Contra, Metal Slug, Magic Sword
Sandbox survival: Minecraft
Shooter: Gradius, R-Type, 1943
Space Simulation: TIE Fighter
Sports: Tecmo bowl, Madden, NBA 2k
Stealth: Metal Gear Solid
Survival Horror: Resident Evil
Tactical RPG: Final Fantasy Tactics, Jagged Alliance
Turn-based Strategy: HoMM
I would add several other genres:
Flight Simulators
Other Simulators/ VR
Casino games
Traditional board games (Talisman, Chess, etc)
Sim: The Sims
City Builders: Sim City, City Skylines
God games: Populous
Tycoon games
Tactical wargames: Gettysburg
Civ games: Civ
4X: MoO
MOBAs
Eroge: Sengoku Rance
Visual Novel
Grand Strategy: EU IV
Music/ Educational games: Guitar Hero, etc...