I have a family. My wife and I are both gamers and have been for years. As I've said in earlier posts, our ability to kill each other without fear of actual injury or abuse charges is one of the reasons we get along so well. Gaming is a serious part of our lives, as much as professional sports might be to other households.
We have two daughters however that are too young to really start gaming. The oldest is three and has had little experience with the controller or the keyboard proper. The youngest is nigh on 2 months old and doesn't even understand her own appendages as of yet. I hope that they show an interest in gaming as my wife and I do, but I can't be certain they ever will. They may see it as Mom and Dad's weird geek thing or they may even actively campaign against games altogether.
Naturally, I've spent a good deal of time thinking about how to avoid such a future. I've almost obsessed over it for weeks with a Doc Brown like fanaticism. After some thought, I've built a framework that I hope will encourage our kids to make games a larger part of their lives. Maybe you can use it too.
Family games come first. By family games, I mean games that everyone can play. Rock Band, the LEGO games, and Munchkin are all great games that anyone can play. Everyone can enjoy the game simultaneously. Halo may sound like fun but if the whole family can't play together, it'll have to wait until the kids go to bed.
Second, encourage your kids to ask questions about the games they see you playing. I can't wait to hear the questions they'll ask after watching me play Shadow of the Colossus. "Daddy, why did you kill Snuffleupagus?" To save the princess, sweetie, to save the princess. Honestly though, it's important for your kids to understand the games they see, even if they are a little high concept for their age. I they ask about Kratos, tell them the truth. Your kids are smarter than you give them credit for, I can guarantee you that.
It's equally important that you understand what your kids are ready to play. The ESRB makes for good baseline ratings, but every child is different. You might have a seven year old mature enough for Grand Theft Auto, it just depends on their attitude and understanding. Really take a close look at what your children sees daily. It'll help you understand what your kids can handle.
Finally, listen to your kids. If they don't want to play, don't force them to. If they want the biggest new release, don't get them the cheap knockoff. If you can't afford it, don't buy it and leave it at that. Gaming is a hobby and an art. Art isn't bought with rent money. If you can afford it and they've earned it, get it. You'll deepen their appreciation for the medium and who knows, maybe you wanted it too.
You can't force your kids to like games. You can raise them in an environment that includes games and is accepting of them. The rest is really up to them. Let them make the decision. If they don't care for Call of Duty, as much as it might break your heart, let them choose whether or not they play. The best you can ever do is listen to your kids and respect their decisions. They may be your kids, but they're human beings too.