Genre, as applied to Video Games, customarily describes the style of gameplay rather than that of the story or setting as in other media. Many games mix and match among them.
It is also possible to move from one gameplay style to another within the same game, e.g. Mini-Games, vehicle sequences within action games, etc. These gameplay changes can sometimes be unnecessary or unwanted, especially if the game transitions between them jarringly with poor integration between them.
Notable games in each genre can be found on the individual pages. Note that many games can and should be in multiple genres, as the lines can often get blurred, or games can incorporate elements of more than one genre. If you have a new game to add, put it in every genre you think it belongs! There are other, more thorough, game databases.
Also see Pinball, the arcade predecessor to Video Games.
These are the genres a Videogame can be classified as:
4X (4X): A game that has four simple goals, which are eXplore, eXpand, eXploit and eXterminate. Sub-genre of a Strategy Game.
Action Adventure: A game that combines parts from Adventure Games and Action Games together.
Construction And Management Games: This type of game focuses on elements like gathering and management of resources, construction, expansion, research and exploration.
Cute 'em Up: A Shoot Em Up that casts the enemies as cute things such as kittens, candy, fairies, and so on. Sub-genre of an Action Game.
Dating Sim: A game in which the player courts at least one potential lover, and the player must keep track of every character's feelings about them and giving out presents, which will feel like a Role Playing Game.
Digging Game: A game in which the player digs through terrain while minding falling objects.
Exergaming: A game that encourages the player to exercise and to get into shape.
Falling Blocks: A game in which blocks fall from the top of the screen, requiring the player to move and flip them so that they'll be arranged in a way to make them disappear, and if the blocks reach the top of the screen then the game ends.
Fighting Game: A game that has a martial arts duel. Sub-genre of an Action Game.
First-Person Shooter (FPS): A game in which the perspective is through the eyes of the player character, and the action revolves around shooting. Sub-genre of an Action Game.
Flight Sim: A game in which the player flies an airplane as realistically as possible.
Full Motion Video (Interactive Movie): A game that is based around video clips, and the player must press buttons at the right time, choose the right sequence of clips, or play other games using the video as a backdrop. Sub-genre of an Adventure Game.
Hack and Slash: A game that has the player character wield primitive, close range melee weaponry, and the goal is to kill as many enemies as possible.
Hidden Object Game: A game in which there is a photorealistic cluttered scene and the player must find and click on a series of objects in it.
Match Three Game: A game in which the player must match three objects of similar color/shape/species to eliminate said objects from the playing field.
Maze Game : A game that takes place in a maze, and the player must either get from one side of the maze to the other, or clear it of every item that won't kill the player.
Mecha Game: A game that focuses on Humongous Mecha for combat.
Metroidvania: A game that combines parts from Adventure Action Games and Platform Games together.
Minigame Game: A game that has a series of puzzles, challenges and games with very different requirements for defeating them.
Miscellaneous Games: A page that contains games that nobody could identify the genre of. It really should be cleaned out.
Mons Series: A game involving the use of different creatures to battle.
MUCK: A Multi-User Text-Oriented Game that emphasizes roleplaying and player intervention.
Multiplayer Online Battle Arena (MOBA): A game that has teams of players competing with each other, typically using the point-and-click interface of a Real Time Strategy; but, unlike RTS games, players control only one Hero Unit instead of a military-industrial complex.
Multi-User Dungeon (MUD) and MOO: An Interactive Fiction that allows multiple (perhaps thousands) players to play at the same time.
MUSH (Multi User Shared Hallucination): A MUD that is just a series of rooms, with players given the bare minimum of interaction systems and let loose to create and manage their own roleplaying.
Party Game: A Minigame Game in which two to four players compete against each other in a boardgame-like environment.
Platform Fighter: A fighting game that has great emphasis on maneuverability on dynamic stages.
Platform Game (Platformer): A game that is about leaping over or onto enemy characters and between platforms of varying heights.
Point-and-Click Game: A game in which player interacts with the environment by moving the mouse cursor over areas of the screen and clicking on them.
Pop Up Video Games: A game in which clicking on background items results in cute animations.
Programming Game: A game in which the player has little to no direct control over the game's events, and must set up the solution, then hit a "go" switch to activate the solution and see if it accomplishes the task correctly.
Puzzle Game: A game that requires mental skill as well as, or instead of, dexterity and quick reflexes.
Puzzle Platformer: A game that combines parts from Platform Games and Puzzle Games together.
Racing Game: A game in which the player drives a vehicle of some kind and races against either other players or time.
Rail Shooter: A game in which the computer controls most of your movement and you control the shots.
Raising Sim: A game in which schedules for a game to process are applied, which in turn affects characters in the game, who then develop 'on their own' without constant user interference.
Real-Time Strategy (RTS): A game that focuses on construction and control of a fighting force in battle that takes place in real-time.
Rhythm Game: A game that will flash commands, and the player has to input the same, synchronized to a beat or melody.
Visual Novel: Even though people equate this with "Dating Sim", they are not the same. Unlike Dating Sims, Visual Novels are more like Adventure Games that allow you to choose your own adventure and get different endings based off of your choices. Sub-genre of an Adventure Game.
Western RPG: A North American or European game that features a customizable featureless protagonist.
Wrestling Game: A game that simulates Professional Wrestling, with grapples, holds and throws.
There are several modifiers that can be applied to the genre of a game, as a twist on the standard formula. These include:
Asymmetric Multiplayer: A multiplayer mode in which different players have totally different roles and capabilities.
Massively Multiplayer Online: A Role-Playing Game that has hundreds, thousands, or even hundreds of thousands of players all connected to it through the Internet.
Meta Multiplayer: A multiplayer mode in which players are playing their own game at a time, but other players are doing this as well.
Minigame: A separate game present inside the main game. May or may not be relevant to progressing through the main game itself.
Museum Game: A game that is primarily about paying tribute to or heavily referencing a franchise or company's past.
Music Player Game: A game in which the levels are generated procedurally from the music you feed it, typically the more intensive and loud the music, the more action you are going to see.
Physics Based: A game that is primarily about the developers showing off applications of physics.
Real Time: When one minute of gameplay equals one minute in game time.
RPG Elements: A game that isn't a Role Playing Game, but the player character is gaining experience points and levels like in an RPG.
Side View: A perspective that views all objects from the side and nowhere else.
Tactical Shooter: A game that resembles a First-Person Shooter, but it features realistic magazines, realistically damaging bullets, Squad Controls, Subsystem Damage, cover mechanics, situational awareness aids, mission planning and no jumping allowed. Sub-genre of an Action Game.
Three-Quarters View: A perspective that is a tilted bird's eye view perspective in which both the top and front of an object is seen at the same time, and the vertical axis indicates both height and depth.
Top-Down View: A perspective that views all objects straight and nowhere else.
Turn-Based: When the player and the computer take turns in making moves.
Turn-Based Combat: A game that isn't an all-out turn-based strategy/tactics but switches to turns whenever combat starts.
3D: When a video game series goes from having two-dimensional sprites to having three-dimensional polygons.
Wide Open Sandbox: When the massive open world and optional material outweigh the actual, goal-oriented gameplay.
And also a number of particularly distinctive ways a game can be marketed or categorized:
Allegedly Free Game: A game that you can play for free, but you will have to pay money to access other game areas or get particular abilities and items.
Beta Test: A development version of the game, built to test how the various components of the program interact with one another and the computer. Some developers have an "Open Beta" process, giving access to a pre-release version of the game to the general public (or playtesters selected from a public pool) for more extensive testing.
Downloadable Content: Additional, optional content provided by the developer via digital distribution and purchased separately from the main game.
Episodic Game: A game that is divided into separate episodes, and allows for cheaper prices, shorter wait times, and shorter development times.
Expansion Pack: Additional content released after the original game that is purchased separately and (usually) requires the original game to run.
Freemium: A game that you can play for free, but if you pay premium then you'll get full access to features that you couldn't get for free and remove advertisements.
Freeware Games: A game that can be downloaded and distributed legally for free.
Game Mod: Third-party modifications applied to an existing game. Can range from cosmetic improvements to additional fan-created content to full-on total conversions that only share an underlying game engine.
Game Mod Index: This is where you'll find Game Mods listed in one place.
H-Game: A game that features sex or heavy fanservice.
Indie Game: A game that is developed without the backing of a publishing company, thus making it independently developed.
Licensed Game: A game based on an existing property, usually a movie, TV series or comic book.
Microtransactions: A game that has individual, one-off payments for accessing additional content in a game.
Mission Pack Sequel: A sequel with so few changes from its predecessor that it feels more like an Expansion Pack than a "true" sequel.
Perpetual Beta: A game which undergoes a long process of bugfixes, tweaks, and rebalancing even after its official release. So named because the developers seem to be "outsourcing" their beta testing to the player base without telling them the game's not really finished.
Romance Game: A Japanese game in which the primary goal is to establish a romantic relationship between the Player Character and one or more of the NPCs.
Shareware: A game that can be played to a certain extent without purchasing it. Buying the game will allow the player to play it to completion, instantly picking up exactly where they left off upon purchase without the need to install anything.
Shovelware: Software that is normally sold in bundles of several products, but it can refer to lowest-common-denominator software in general.
30-Day Free Trial: Software which you're allowed to use for a fixed, limited amount of time without paying for it. Once that time expires, you must send money to continue using it.