I think sometimes we have can have a tough time connecting with our kids.
The trick is to subvert your children into becoming just as nerdy as you are by playing table-top games with them (the best solution too IMHO [insert evil laughter here]).
Clearly your kindergardeners aren't ready for D&D or GURPS, but they may be ready to play some other games that are more tailored for them. Here's a list of games that are perfect for the nerd parent looking to spend some quality time gaming with their kids. If you have played any of these, or have other suggestions - please let me know in the comments.
Faery's Tale (Ages 6+)
Board games I've done, but this will be my first foray into RPG gaming with my kids. I figured, any game designed by Robin Laws is worth taking a look at; plus my son is the ripe for "gaming with dad" as his puts it. The Wii is fun, but it gets old fast.
Faery's Tale is a simple introductory table-top roleplaying game where the players choose to be pixies, brownies, sprites, or pookas in the realm of Brightwood. The game uses six-sided dice for rule mitigation and includes three adventures for you to get started. The rules are straightforward and easy to understand, so they don't get in the way of the game's storytelling style of roleplaying. Also, the genre (fairies, elves, and woodland creatures) works well with both boys and girls - which I consider a plus. In addition, the game seems to allow for full-campaigns to develop, which will appeal to older gamers who are looking continuity between games. Faery's Tale is available as both a softback book from Amazon.com (Faery's Tale Deluxe) and as a PDF eBook from RPGNow.com. Once we get a family game started (waiting till after the holidays), I'll likely start a campaign log here on The Core Mechanic so that you can get a feel for how it plays out.