As a general rule of thumb in our house, we allow our kids 2 hours of "screen time" a day. They can choose to use their screen time for TV, computer games, or GameBoy/Nintendo DS.
When they choose computer time, they have several online destinations that offer some amazing high-quality games starring their favorite TV, movie, and toy characters - all completely free. Here are a few of their favorites (side note: kids love to be interviewed about stuff like this):
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The games are great, and I'm thrilled with the price, but I'm a little concerned that they'll end up browsing to some less kid-friendly sites on the web while I'm not watching. They wouldn't do that intentionally (not yet anyway), but the possibility is there as they get older and learn to use the browser to explore other online sites like youtube or myspace.
It's impossible and impractical to monitor everything our kids do online (who has time to sit behind their kid for a half hour while they play on the computer??), so we also encourage them to check out games on CD from their school library, which they do. Still a great price (free), but they have to return them in a week or so.
I also recently learned about the Family Savings Outlet, where we can get popular game titles delivered on CD for a very affordable price ($4.95 each and just over a dollar for shipping). They have software for both fun and learning, with titles that are targetted to specific age groups.
It's nice that there are several options for screen time, but I think it's also important to encourage some regular board games - ya know, the kind where you actually sit down and play with each other, in person.
Our two favorite family games are Uno Spin and Zooreka. They're loved by everyone from our 5 year-old son to our 9 year-old daughter, and are fast paced enough to keep everyone's attention (even mine).
The real reason they love the games though is because it's a chance to hang out with dad (and mom too). For me it's a chance to turn off work and have fun with my kids, while helping them become better competitors - gracious when they win, and respectful to each other when they disagree with a play.
Which reminds me - it's been a while since we had a family game night. It's definitely time! 
