There are numerous educational games on the market that are geared for specific age groups. Math, spelling and science-based games can give children excellent foundations to build their schoolwork on.
Puzzle video games help children learn how to become problem solvers and reason through steps needed to solve a problem. They also encourage kids to think ahead to the consequences of their immediate actions.
Matching video games (especially when this is a game-within-a-game scenario) can help kids hone memory skills. Many of these games are also timed, making kids think fast if they want to reach the next level.
The world of gaming is far from gender neutral, and many games--even those for primary-school age children--depict women in a negative way. It's important to make sure that impressionable children aren't playing games that teach them that women are not created equal.
Video games build hand-eye coordination, a skill that's often necessary to progress within a game.
One thing video games lack is a component of social interaction. It's important to make sure that children know how to relate to other people as well as they can relate to the TV or computer screen.