I don't have kids, but it was my stepfather who got me into gaming (though it was inevitable, anyway), and when I have kids, I would like to introduce them into gaming the same way.
I have a daughter who is 7, and a son who is 5. My friends and I just started played at my house (my buddies basement flooded). Well, after my bambinos watched us play, they begged me to teach. Since D&D is a little too complicated for them, I used my son's small Digimon figures and let them roll up stats. Afterwards we had a battle royale. I am currently making some special attack cards that they will draw at the beginning of the game, and can use throughout. Maybe a D4 worth at the start. Either way, just a few more years! Great deal on the Big Brother thing.
I have 2 children. Almost 3 yr old daughter (May 9th) and an almost 2 month old son (born X-mas Day) the daughter is currently playing a halfing barbarian prophet who speaks only in some outlandish language that the players don't understand. An oracle she isn't. The boy is just now getting ready to be "born" into the game world as a new god... the god of sloth and spitting up. . we also have one of the members son in the group he is 12 and he doesn't pay attention too well.
No kids, but when I do I'll sure as hell try and give them a favorable introduction to the hobby. After all, I wouldn't be gaming today if a friend's dad hadn't dragged out the old 1E core books and run us through a few sessions.
I voted Yes, but should note that they aren't old enough to play a "structured" game yet.
On the other hand, I have managed to ingrain the concept of fairness and pre-determined boundaries, which should allow for a smooth progression into concepts of balance and rules later.
I'm also reading the first Harry Potter to my oldest (5).