For my son's first (6 years old) foray into D&D, and to play to his interest in all the crazy dice, I borrowed a page from the old Dragon Strike game and made it so that all abilities and checks were set to different dice (d4-d12) depending on how good you were at it. For magic and special abilities he had a hand of cards (with text, pictures, and icons) that operated off the standard at-will/encounter/daily mechanics.
I also patterned the game (as well as each of the first 3 or 4 little mini-campaigns I ran for him) very heavily off of what his primary TV/movie/video game interests were at the time. The first had been a Pokemon/Legend of Zelda kind of game where he basically played Link as a Ranger who could capture different monsters he was fighting in Pokeballs and use them later as animal companions. The second was a Ben Ten styled game where he could temporarily change into different legendary heroes that had been trapped inside of cursed story books. The third, probably first "true" D&D game he played, was about a mild mannered half orc barbarian called The Incredible Rulk who had a bunch of rage abilities.
I also am always a really big fan of doing a lot of "and then what happens"-ing story building when I run games for kids.