First Person Shooter: A game in which the storyline is played from the player's point of view, and the player usually (but not always) has a weapon of some sort. Perfect example: COD (see #4)
Role Playing Game: usually lengthy games with a storyline, often involving some sort of quest. It usually involves leveling your character, like making her/him stronger, faster, etc. Example: WoW (#5)
Call of Duty: An extremely post popular combat video game. It was originally based off of World War II, but has since expanded to other armed conflicts.
7. Open World
A type of game that allows the player essentially limitless access to the entire virtual world. Example: Grand Theft Auto