I love Shadows as a first introduction to role playing for kids. This example of actual play will give you and idea what to expect if you try this at home.
My Shadows review has more details on the game, but the basic mechanic is that a player decides on a good outcome of taking an action and a bad outcome of taking an action. They roll two six-sided dice, colored light and dark. If the dark die is higher, the bad outcome happens, otherwise the good outcome happens. At three, my daughter wasn't counting yet, but could distinguish the higher die based on the number of pips showing. If you're doing this with kids who aren't counting yet, use dice with pips, not numbers.
The typical opening to a Shadows game is that the players play themselves, and are wakened by a noise. From there the game evolves based on input from everyone, so it's more cooperative storytelling than traditional role playing.
Here's our actual play:
Me: You are sleeping, and are woken up by a loud noise.
Amelia: I go see what it is!
Me: It's a large truck backing into our driveway.
Amelia: The food truck! I go help unload.
Me: You have to open the door for that, which is hard for you so you'll have to roll. What do you want to happen as a good outcome?
Amelia: I get the door open and go out to help.
Me: And what do you want to happen as a bad outcome?
Amelia: (thinks) I can't get the door open. (Rolls the dice, the light die is higher)
Me: You open the door, and go out to the truck.
Amelia: I help unload!
Me: The boxes are pretty heavy, so you'll need to roll. What is the good outcome?
Amelia: I find a light box and carry it into the garage.
Me: And the bad outcome?
Amelia: The box is too heavy! (Rolls, and the dark die is higher)
Me: The box is too heavy. What do you do now?
Amelia: Ask Mommy for help.
Me: Okay, Mommy comes to help you carry the box into the garage.
And it goes on from there, but that's enough to give you an idea how it played out. I learned some things from this early experience.
Role Playing Versus Playing
Kids can only role play based on what they know. We've limited TV in our house, so Amelia's experiences to draw on are mainly based on what happens in her life.
What was most interesting to me was that when Amelia plays, she invents all sorts of fantastical happenings. Flying horses getting stuck on the ceiling, were-tigers that change into cats and back into tigers, etc. But when she role played, she limited herself to what normally happens in her life.
I don't know if this is developmental, or due to the fact that in Shadows you normally play yourself. I plan on trying again and letting her pick what character she wants to be, and see if she brings more of her play world into the role playing.
Regardless, though, role playing parents who want to encourage the tendency in their kids could do far worse than to introduce Shadows at an early age.