Genre
A genre is a set of criteria for distinguishing different games from one another in terms of types of gameplay.
Action
Action games are largely defined as reflex-based games that typically feature a lot of violent force. Platformers, Shoot 'em Ups, and Beat 'em Ups are considered part of this genre.
Games of this type include Super Mario Bros. and Super Metroid.
Adventure
Adventure games are characterized by exploration, puzzle solving, and interaction with game characters. Games of this type are focused more on narrative than reflex-based challenges.
Games of this type include Legend of Zelda.
Puzzle
Puzzle games, as their name implies, are based on puzzle-solving to find a solution. This can include a multitude of gameplay types, though most tend to be based on Tetris-like play.
Games of this type include Dr. Mario and Tetris Attack.
Racing
Racing games are speed-based with first place typically being the goal. Exceptions often exist, such as in score-based games like Excite Truck. A subgenre of Racing also includes Kart games, which employ weapons to be used during a race.
Games of this type include F-Zero and Super Mario Kart
Sports
Sports is generally a broad genre that incorporates a multitude of real-life sports set in a realistic or fictional setting. Racing games are generally not considered part of the sports genre.
Games of this type include Mario Tennis and Super Mario Strikers.
Strategy
Strategy games are typically ones that rely on planning and tactics, most often used in war games. These games tend to rely very little on luck and can either be Real-Time games or Turn-Based.
Games of this type include Advance Wars and Pikmin.
RPG
Role-Playing Games (or RPGs) are games that generally are composed of a group of characters that increase in power, usually through a means of experience, throughout the game.
Games of this type include Fire Emblem and Pokémon.