Genres

Action Games
Action-Adventure Games

Adventure Games
Beat'Em Up Games
Choices-and-Consequences Games

City-Building Games

"Endless" Games (Endless Brawler, Endless Runner, etc.) 
Fighting Games
Horror Games
Interactive Fiction
Interactive Fiction with Graphics
Maze Games
Motion-Sensing Games
Open World Games
Party Games

Platform Games

Puzzle Games

Racing Games

Rhythm Games
Role-Playing Games

Shoot'Em Up Games

Sports Games

Survival Games

Strategy Games

Virtual Reality