I'll second Lego Star Wars...at least the second one for the 360...I haven't played the original for the old XBOX. I'm playing it with my 5 (and 1/2) year old, and it's pretty fun.
Like the other guy said, you can die as many times as you want, and it restarts you right where you left off. I think it's easy enough for kids, but it's also funny and entertaining enough for adults, and there's plenty of goals and hidden characters and vehicles and missions to get also. Plus it's legos...and star wars...they go together like chocolate and peanut butter.
The other game I have for him is Cars, based on the movie. It's non-violent, and there's no dying/shooting etc in it. It's also pretty easy for kids to pick up and play, but also has a lot of goals in it to go do, as they get better at it.