All Game Genres on Wikipedia
I went through all the subpages from the game genre page of Wikipedia listed them accordingly and then I removed all duplicates. I'm planning to make a singular post for almost all of these going into detail about the elements they use so you know how to implement them. Just search the 'genre' label to find the respective posts.
1 Action
1.1 Platformer / Jump 'n Run
1.1.1 Puzzle-platform game
1.1.2 Run 'n gun game
1.1.3 Cinematic platformer
1.1.4 Comical action
1.1.5 Isometric platformer
1.1.6 Platform-adventure
1.1.7 Endless Running
1.2 Shooter games
1.2.1 Shoot 'em up / STG / SHMUP
1.2.1.1 Fixed shooters
1.2.1.2 Rail shooters
1.2.1.3 Tube Shooters
1.2.1.4 Scrolling Shooters
1.2.1.4.1 Vertically scrolling shooters
1.2.1.4.2 Side-Scrolling Shooters
1.2.1.4.3 Isometrically scrolling shooters
1.2.1.5 Multidirectional shooters
1.2.1.6 Bullet Hell
1.2.1.7 Cute 'em up
1.2.1.8 Run and gun
1.2.2 Shooting gallery
1.2.3 First-person shooters
1.2.4 Third-person shooters
1.2.5 Hero shooters
1.2.6 Tactical shooters
1.3 Fighting games
1.4 Beat 'em up games
1.5 Stealth game
1.6 Survival games
1.7 Rhythm games
2 Adventure
2.1 Interactive fiction
2.2 Interactive movie
2.3 Visual novel
2.4 Dating Sim
2.4.1 Eroge
2.4.2 Bishojo
2.4.3 Otome
2.5 Escape the room
2.6 Action-adventure
2.6.1 First-person action-adventure
2.6.2 Third-person action-adventure
2.6.3 Immersive sim
2.6.4 Platform-adventure games
2.6.5 Isometric platform-adventure
2.6.6 Stealth games
2.6.7 Survival horror
2.6.8 Survival games
2.6.9 Metroidvania
2.7 Graphic adventures
2.8 Real-time 3D adventures
3 Role-playing
3.1 Action RPG
3.1.1 First-person dungeon crawl
3.1.2 Point and click
3.1.3 Role-playing shooter
3.2 First-person party-based RPG
3.3 MUD
3.3.1 Hack 'n Slash MUD
3.3.2 PvP MUD
3.3.3 Roleplaying MUD
3.3.4 Social MUD
3.3.5 Talker
3.3.6 Educational MUD
3.3.7 Graphical MUD
3.4 MMORPG
3.5 Sandbox RPG
3.6 Tactical RPG
3.7 Roguelikes
3.8 Fantasy
3.9 JRPG
4 Simulation
4.1 Construction and management simulation
4.1.1 City-building
4.1.2 Theme park management
4.1.3 Colony management
4.1.4 Business simulation management
4.1.5 Government simulation management
4.1.6 Sports management
4.2 Life simulation
4.2.1 Digital Pet
4.2.2 God
4.2.3 Social simulation
4.3 Sport
4.3.1 Arcade
4.3.2 Simulation
4.3.3 Management
4.3.4 Multisport
4.3.5 Sports-based fighting
4.3.6 Racing
4.4 Vehicle simulation
4.4.1 Flight simulator
4.4.1.1 Amateur flight simulator
4.4.1.2 Combat flight simulator
4.4.2 Space flight simulator
4.4.2.1 Space combat
4.4.2.2 Space trading
4.4.3 Submarine simulator
4.4.4 Train simulator
4.4.5 Vehicular combat
4.4.6 Farming simulator
4.4.7 Boat and naval simulation
4.4.8 Tank and mech simulation
4.4.9 Trucking simulator
5 Strategy
5.1 4X game
5.2 Artillery game
5.3 Real-time strategy (RTS)
5.4 Real-time tactics (RTT)
5.5 Multiplayer online battle arena (MOBA)
5.6 MMORTS
5.7 Tower defense
5.8 Turn-based strategy (TBS)
5.9 Turn-based tactics (TBT)
5.10 Wargame
5.11 Grand strategy wargame
6 Other genres
6.1 MMO
6.2 Casual games
6.3 Party game
6.4 Programming game
6.5 Logic game
6.6 Trivia game
6.7 Board game / Card game
6.8 Serious game
6.9 Educational game
6.10 Exergame
6.11 Electronic sports
7 Idle gaming
Wikipedia Doesn't List All
Wikipedia is a website where humanity can accumulate information. So, new genres that are created on the go are not listed here. Also, there might be more subgenres that either haven't been named yet or focused on. Since - technically - you can create a genre of any individual game once there are multiple similar ones. Another thing is that you can categorize games by graphic style. Like the genre of 8-bit games or something. However, the ones listed and used nowadays usually describe the game elements and gameplay.
