We've tried several RPG's for kids, but so far, my children have liked rpgKids the best. Some reasons why they responded well to it:
First, the entire ruleset comprises 4 pages, with one page of optional rules. The rest of the PDF gives advice on running games with kids, a full-length adventure, character sheets, colorful tokens and maps, etc. So, the simplicity of the game is probably one of the strengths to which my kids responded. Combat consists of a simple opposed roll. The game employs classes that are abstracted into three categories: melee, ranged and magic. The classes themselves are also rather abstract (Healers, Sword Fighters, etc.) with minimal characteristics to differentiate them. There are no attributes (i.e., no STR, DEX, etc.) to track. There are no hit points or weapon damage points, because every attack (melee, ranged or magical) does the same damage: Once a PC or monster is hit once, he is considered "Hurt," and if hit twice, he’s "Knocked Out." There's a simple healing mechanic to allow PC's to get back into the fight.
The simplicity might make the game sound dull, but I found that it allows the GM (presumably an adult) to shape and adapt character concepts and actual gameplay for dramatic effect, a mechanic which the game encourages. As simple as the game is, it wasn't always a cakewalk for the PC's to accomplish their goals, so having the freedom as a GM to do a bit of modification (and even hand-waving on occasion) to maintain drama and keep the story moving is a strength, I think.
One last thing which differentiates rpgKids from other kid games is the quality of its adventures (there's an Adventure Pack, in addition to the full adventure included in the game). Mind you, we're still talking about adventures written for 4-7 year olds, so have realistic expectations. However, unlike the insipid nature of the adventures in some other kids rpg's, these have depth, both in terms of gameplay and story. No insipid rat hunts in cellars!
My kids thoroughly enjoyed rpgKids. They were able to quickly grasp the nature of the character classes and adapt them to suit their needs (e.g., a Sword Fighter is easily shaped to be a mace-wielding dwarf, a Healer can be a robe-wearing priest, and a Wizard can be Gandalf or some necromancer). They were also able to quickly get into the action -- not bogged down by rules, they let their little imaginations fly. As GM, you just roll with their moves, and fun is had by all.