Keeping the computer in a central location is probably the best bet in monitoring what a child does when they're online. Our computer is in the den, where it can be seen from the living room. Granted, my son is only 6, and doesn't do much of anything online, it will definitely be beneficial when he gets older.
Molly, I have to agree with your assertion that NetNanny type programs that block bad websites are not the way to go. Here are my tips on how to keep your kids safe online:
First, Education! tell your kids not to share personal information -- make it specific about what not to share and tell why. Include examples like how a person could figure out where you live if you give the name of your school, or the school's football team name, etc., esp. someone who meets you and develops a relationship with you online in a forum or some such place.
Second, Supervision! My husband (the interior decorator in our house) hates the fact that our main computer is in the kitchen. I'ts right there, next to the kitchen table. In fact, if you rotate the computer chair 180 degrees, you're sitting at the kitchen table (thought it's often quite difficult to get the kid to quit out of the game and actually make the chair rotate when it's time for dinner!). I think it was the best move we've made in the way of furniture rearrangement. It makes it very easy for me to know what the kids are doing on it. Now that we have a laptop, I make it a point to drop in frequently if the kids are using it in their bedrooms. But, my husband and I get first dibs on the laptop so the kids are more likely to use the desktop computer anyway.
I thought I'd share this since none of our hosts seem to have kids, so they don't have first-hand experience in this.