A bunch of arcade games become much more friendly to kids with infinite continues, shmups, fighters, brawlers, etc but for those you'll need to filter on violence. I'd probably also avoid anything RPG or story heavy.
My picks would be Bubble bobble, Kirby on SNES, ice hockey on NES, Mario 1-3, super Mario kart, Tetris, monkey ball, Dr Mario. For Sega Sonic 1-3 & knuckles, ecco, robotnik's mean bean machine, Alex kidd, outrun