Wow, going back and picking out NES games to recommend is tough. Especially with the added caveat of trying to be low on violence (I agree that Double Dragon is probably not appropriate, and for similar reasoning one would probably have to nix other classics like Contra, Ninja Gaiden or River City Ransom). I also suspect it's probably inappropriate for various reasons to recommend games that require an extended time commitment to finish, such as The Legend of Zelda, Final Fantasy, or probably even Mega Man games (all of which are still pretty enjoyable even today). So, here're my recommendations:

-Tetris and clones (Dr. Mario)
-Rampart
-Excitebike
-Spy vs Spy (some comic violence)
-Arkanoid
-Galaga
-Gradius
-Pacman
-Millipede