You want / need / crave / desire / demand
Moonbase Commander. It's a multiplayer turn based strategy game that's easy for anyone to learn how to play. I've always seen it packed towards the kid's software in stores but I wound up giving it a go via GameTap and got hooked very quickly.
For the slightly older kids interested in some run and gun gameplay but with a much friendlier twist, you can look into
Nerf Arena Blast. I guess it depends on how picky you are about the "no guns" rule or if it's possible to extend it to the "Lego Rule" (no real weapons, no real violence)
Re-Volt might be worth looking into for another racing game as is
Sonic R, which is easy as hell to find on the extreme cheap (you're much more likely to find it bundled with about 20 other Sonic games for a grand total of like $15 than you are to find it on its own).