There is a lot of concern in the media and in the general population that games, and computer games in particular, may be bad for the mental development of children. This leads a lot of parents to ban consoles from their homes and forbid their children to play them around their friend’s houses, but this may be slightly misplaced, as studies are fairly mixed on how harmful it is.
In fact, studies are pretty much evenly divided on the matter, although both sides of the argument certainly agree that there are games that kids should not be playing. This is something which is being addressed by age recommendations on games, but they still aren’t observed reliably.
If you want to make sure that your children are not being harmed by the games they’re playing, the minimum you should do is observe the age requirements on games. Getting games which try to enhance their learning, or which challenge their brains, is another way to let them experience games without risk.