Doudou Linux: Ages 2 and Up
Doudou Linux is based on Debian 5 and thus it's quite stable (and also means that if you know your way around Linux, you can install programs from the Debian repository). The desktop environment is reworked completely to make it as easy as possible for children. Doudou includes Child's Play and GCompris, two popular collections of Linux games for Kids. In addition, Doudou Linux offers adventure, arcade, board, card, logic and sports games to enjoy, Geography, Kanagram, Hangman KLetters for learning, Instant Messaging (Empathy) and Web Browser (Epiphany) for surfing. These programs are grouped under "Learn", "Work" and "Enjoy" sections and arranged in a neat, tabbed interface.
Doudou Linux is currently very young, but the passion of the contributors, especially from France and Russia, signals a future very strong child friendly Linux distribution. (There is an extensive review of Doudou Linux already in my hubfolio.)
Note: Their last update seems to have been in June 2010.