BZFlag is a multiplayer internet battlezone capture the flag game.
Game play is simple: use mouse for movement and to fire. Use tab to jump, but that is not required. My 2yr old likes it even though he never frags anyone, I expect a 4yr old could play it and do ok.
Game play is Internet based normally with chat, so folks can say what they want. Sometimes the conversation is not too child friendly.
The game is good for teaching mouse skills. It can be played with the keyboard as well, but the mouse is better.
?TimRikern the project maintainer says: We have added chat "filtering" to the client and server. This include a list of "bad words" that if found in messages are not be displayed. You can also disable chat in the client configuration.
The long term plan at present is to develop a "karma" system and have peer ranking so that the community could govern itself with kicks, bans, etc.