Some people have a problem with letting their kids play any and all video games at age 4 believing it's detrimental to a child's development but I really believe there are important character building and problem solving skills that a kid can learned playing the right games.
here's one of my kids favorite games and what I believe she gets out of playing it:
Scott Pilgrim vs. the World (PS3)
This retro side scrolling 2D beat-em up is simple enough so that most kids can pick it up and play with a parent or a friend. It's beautifully rendered levels and cute character designs are endearing. Level progression is tough on your own but with a second player it becomes a bit easier.
It's a great game that helps your kid understand teamwork. Before you dismiss me as a gamer nerd dad gone mad, just hear me out. It's a multi player game that requires my child to come to the aid of a fallen comrade and resuscitate them in order to progress to the next level. You can also team up to help one another in and some levels require to keep the enemies distracted while the other person runs around collecting coins that you can share in the store to upgrade your favorite character's attributes.
So you get team work, selflessness, counting, patience, hand-eye coordination and learning how to be a gracious loser, a skill that if you've played anyone online, many adults have yet to learn.
I really love this game and further more I love playing it with my child.
Baby No: 5/5
here's a glimpse of the game in action in case you where thinking about getting it.