I'll recommend a couple of games no one has mentioned yet:
Rayman Raving Rabbids - This is a mini-game compilation with lots of character and funny bits. It has rhythm based sections where you follow the beat of a song and get dancing bunnies as rewards of your success. It also has some on rails shooting. You shoot plungers at the rabbits so IMO that's not so violent for kids. It also has racing, jump the rope, cow toss, whack a mole (rabbit), and many more. It has a few frustrating mini-games, but the good ones outweigh the bad ones by a lot. The best thing about all this is that you can find this game really cheap almost anywhere. It's currently $15.49 at amazon and if you're ok with buying used games you could get it much cheaper.
Destroy All Humans: Big Willy Unleashed - This is a sandbox kind of game. You're an alien who has to accomplish some missions for your boss. You can go by foot shooting people with several weapons like the disintegrator, anal probes, bombs, and more. You can also ride the saucer and abduct people, destroy buildings and cause some mayhem. And in some missions you control a giant boy robot (Big Willy) and eat people, kill them with your gases and more. This game didn't get good reviews because it seemed like the reviewers liked the previous games more than this one and because it's not too long. I beat it in 10 hours, but I enjoyed every minute of it :). And just like the raving rabbids game, you can find this game for cheap too, I bought it for $15 brand new just to give it a try cause I had heard the other two were pretty good and was pleasantly surprised.
One more:
Mario Party 8 - This one is a collection of mini-games too, but you play on a board and roll dice to move like most board games. It also has good and bad mini-games. I borrowed it from a friend of mine to give it a try and my wife loved it. I guess it is lots of fun with kids too. The only bad thing, IMO is that this game is still very expensive. It still goes for $40 to $50 at most places and I've been waiting for it to be on sale or get a price drop, but like most nintendo titles it just doesn't happen.
Edit:
Damn it, PorkChopTD beat me to it with RRR
