Pardon the dust!
This page includes some jargon that hasn't been added to the site's glossary yet. I'll be around to fix this later, but sorry for the inconvenience in the meantime.

An incomplete list of video game genres

Why is this an "incomplete" list?

We're used to putting our entertainment into neat little boxes called "genres" based on style or subject matter. For example, a movie featuring a silly story is likely to be considered a "comedy", while a slow guitar song about the Old West is probably going to be labeled as a "Country Western" song. We do this with video games too, except that instead of focusing on their style or storyline, video game genres are based around the game's mechanics.

There's just one problem: there are countless ways to play games. The more specific we get when labeling genres, the more it looks like the taxonomic system of the animal kingdom, and nobody is interested in dealing with a list like that. Often, people resolve this problem by using very broad categories or by saying that a game has elements of another broadly recognized genre. As an example, Borderlands is known as a First Person Shooter with "RPG elements". This lets people know that it's similar to games like Doom or Wolfenstein, but unlike them, it also shares some mechanics you'd expect in RPGs.

Because of this inherent problem, not every genre can be covered on a page like this. We can still make a pretty thorough list however, so I've made an effort to summarize most of the more well-known genres below.

Early Genres

In the earliest days of gaming, there were no consoles or home computers. Games were sold in large standalone units called "arcade cabinets". Each arcade cabinet featured only one game, and these games tended to focus on gimmicky gameplay with repetitive level designs. Today, these games are still somewhat popular and have their place in gamer's libraries, but they aren't as gripping or interesting as more modern games.

Ultimately, four genres became popular in the arcades, with their popularity peaking in the 1990s. These genres are:

Arcade
This is the "catch-all" genre for simple games like those that were seen in the early years of gaming. Most of the time, their gameplay is unique to each title, with the levels repeating until the player runs out of lives. The primary goal of these games is to earn a high score and get your name recorded in the game's leaderboards. Famous examples of Arcade games include Galaga, Pac-Man, and Frogger.
Beat 'em Up
More popular in the 1980s than today, Beat 'em Ups like Streets of Rage or Double Dragon used to be popular multiplayer games. These games have the heroes fight all sorts of baddies -- angry gang members, ninjas, mutants, and even crazed robots -- using just their fists and flashy martial art skills.

On a side note, Beat 'em Ups and Fighting games, while similar in many respects, are actually two very different beasts. The simplest way to tell them apart is that Beat 'em Ups have the players wander through levels facing multiple opponents, while Fighting games restrict the action to a tournament or arena setting.
Shoot 'em Up
One of the first major genres to become notable in gaming history was the Shoot 'em Up, or "shump". Often military or space themed, these usually feature the player's ship or plane at the bottom of the screen and waves of enemies coming down from the top. Popular shumps include Raptor: Call of the Shadows and Gradius.

Sometimes this design would be adjusted slightly, with the ship on the left and enemies coming from the right. This alternate style is sometimes known as a "side-scrolling shoot 'em up".
Twin Stick Shooter
In this type of game, the player is able to move in any direction while firing their weapon in any direction. This is accomplished by using two joysticks (hence the name, "twin stick" shooter). One joystick moves the player, while the other one aims and fires your weapon. Games today may emulate this setup by using the controller's buttons as the second joystick, although this isn't always needed as some controllers feature twin analog sticks.

A notable game in this genre is Robotron: 2084, and there's an interesting story behind its development. One of the developers was injured in a car accident, leaving him with his right hand in a cast. This prevented him from playing games that used the traditional joystick and button controls, so he began experimenting with other design ideas, and eventually Robotron's famous control scheme was created.

Console Kings

The arrival of home consoles ushered in a new era of gaming. With their hardware standardized, developers could focus on finding ways of creating new and more elaborate types of games. This led to popularization of a number of new genres, many of which became increasingly specialized within their own niches. Some of these newer games did get their start in the arcades, but it was their console ports that really caused them to take off and become famous.

These newer genres are:

Action
Much like action movies, action games are fast paced and focus on testing the player's mental and physical dexterity. Quick Time Events are commonly seen in this genre, but they aren't exclusive to it. Also, many other genres on this page can be labeled as "action games", despite their more distinctive genre names, as this term can sometimes be shorthand for "it's not a Puzzle game".
Fighting
As mentioned above, Fighting games are slightly different than Beat 'em Ups. The main difference is that Fighting games, like Street Fighter or Mortal Kombat, are focused on short bouts between two combatants. Essentially, this is the video game equivalent of "Rock 'em Sock 'em Robots" -- the only goal in each level is to reduce the enemy's HP to zero before they do that to you.
Platformer
These games have the player's character run and jump from one place to another. Most of the time, there are tiny areas of "ground" hovering suspended in the air. These floating platforms then, gave this genre its name. Platformers are often 2D, but this isn't a strict requirement. There are also many subgenres, such as Platform Shooters, Platform Puzzlers, and Metroidvanias.

Easily the most famous Platformer games in video game history are the main games in the Super Mario Brothers franchise.
Puzzle
Puzzle games are basically what you'd expect. They're about solving puzzles, though the definition of "solving" can vary. These tend to be very family friendly, as there's too much of a focus on playing with tiles or blocks to let any real violence or objectionable material creep in. There are also a handful of related subgenres, such as "Puzzle Platformers", "First Person Puzzlers", "Logic Puzzles", and, of course, Match 3s.

Probably the most famous Puzzle games are Tetris and Bejeweled.
Racing
In the arcades, racing games usually used either a way to fake 3D graphics, or they used a top-down perspective. But, home consoles had better tricks and eventually developed actual 3D physics, so this genre only really took off during the console era. Some of the most famous racing games have been from the Need for Speed and Super Mario Kart franchises.
RPGs
Although every game has the player take on a character's role to some extent, Role Playing Games (RPGs for short) take this a bit further than usual. This is the realm of games like Dungeons and Dragons, Wizardry, Final Fantasy, Dragon Quest, and similar games where numbers and charts are omnipresent. These can also be broken down into many subgenres, such as JRPGs (RPGs from Japan), CRPGs (RPGs like those from old computer games), and Action RPGs (which mix the controls from the Action genre with the mindset of an RPG).

PC Playboys

The rise of home computers also led to new styles of gameplay, as developers had new ways of controlling their games. Or to be more specific, they could now make games utilizing the keyboard and mouse. Since the player could now quickly select any area on screen, it became possible to have the game's GUI do something more than just display information. This led to new ideas and many new genres, most of which also took advantage of a home computer's (at the time) higher storage and processing capacity.

Today, computers and consoles are roughly in the same ballpark when it comes to raw power, but the keyboard and mouse combo can still easily out perform a controller for certain types of games. Here are some of the genres that are mostly found in PC gaming.

City Builder
This genre is all about managing resources and overseeing infrastructure. Most "City Building" games involve running a city or other settlement, but more than a few have taken the same concepts and applied them to managing a park or other business. The most famous games in this genre are undoubtedly those in the SimCity and Rollercoaster Tycoon series.
Edutainment
These games focus on teaching children different subjects through simple gameplay. While there had been some attempts to make Edutainment titles on home consoles, they really only took off on computers. Part of this was because they could find their way into school computer labs, giving children something fun to do during class. Some of the more popular Edutainment games from back in the day were The Oregon Trail, Word Munchers, and Where in the World is Carmen Sandiego? .
First Person Shooter
Easily the most recognized (and most reviled) genre out there, First Person Shooters have the player run around killing things. The name comes from the player's viewpoint: you're seeing the game world through the eyes of your character, as if you were in the game. Thus, you have a first person perspective on the (often extremely violent) action.

The majority of these games have a military or science fiction setting, as demonstrated by Doom and Wolfenstein 3D, which are easily two of the most well-known games in this genre.
Hidden Object
Hidden object games are something of a rarity, possibly due to them having a very niche audience. These games have you find objects that are hidden among other objects and debris in a large picture. The best ones have a story that guides the player from image to image, but this isn't a requirement. This is also such an underrepresented genre that I'm not aware of any well-known or famous games to provide as examples. That said, two of my favorites are Dracula: Love Bites and Romance of Rome.
Idle Games
Idle games are probably the strangest types of games out there. You don't exactly play these games. Instead, you leave their windows open and the game effectively plays itself. You do, however, need to micromanage things from time to time in order to advance the game. The best known example of these games is Cookie Clicker, which bakes virtual cookies while you do other stuff. Once you have enough cookies, you can spend them on various items that will help make you make more cookies. And so on. Forever.
MMOs
Short for Massively Multiplayer Online games, MMOs are online games where thousands, if not millions, of players are playing together via the internet. It's likely that players will only encounter a small fraction of the game's playerbase during their adventures, but one never knows. Exactly how much you're required to interact with other players varies depending on the game in question.
MMORPGs
This genre is a merger of MMOs and RPGs, creating vast worlds where players essentially decide many aspects of their character and their relationship to the fantasy world they inhabit. In many ways, this brings the openness of RPGs to some of the largest multiplayer worlds in history. The most famous MMORPG is unquestionably World of Warcraft.
Point and Click Adventure
Easily the most obvious result from adapting games to the keyboard and mouse control scheme, these have you lead a character (or characters) through an adventure by pointing out stuff for them to interact with. This style of gameplay is slowly becoming less popular, as more and more games are borrowing the controls (but not the content) of First Person Shooters. Popular point and click adventure games include Grim Fandango and The Secret of Monkey Island.
Third Person Shooter
This genre is the sibling of the First Person Shooter. The only real difference is that you're seeing the game's world from a "camera" mounted just behind and over the player character's shoulder. So, instead of seeing things from their perspective, it's like you're standing behind them (ie, a third person viewpoint). Some First Person Shooters can switch to a Third Person perspective and back, so the lines between these genres are very blurry.
Simulation
Have you ever wondered what it might be like to fly a fighter jet, drive a delivery truck, run a garage, or try your hand at being a surgeon? Simulation games are all about this concept, allowing you to play around with otherwise mundane activities. Some of the earliest games in this genre were flight simulators, most famously Microsoft Flight Simulator.
Strategy
Warfare has always had its fans, and nowhere is this more obvious than Strategy games. These are often based on historical events, such as World War II or Vietnam, but fantasy settings are just as common. In these games, players raise vast armies and (usually) try to conquer the world. Occasionally, City Building game elements are mixed in, requiring the player to both govern their military and their nation simultaneously. Civilization, Age of Empires, and even the board game Risk are examples of this type of game.

Also, you might hear about "real time strategy" games when talking about this genre. This specifies that all players are playing in real time, as opposed to the more traditional method of having the players take turns.
Visual Novel
These are interactive storybooks. Their stories change depending on the choices the player makes while reading them, and there are usually a lot of different endings. Unfortunately, this genre is also very heavily tainted by the sheer amount of pornographic visual novels out there. Finding the good ones is not that easy, and many gamers won't play them at all because of the stigma attached to them.