First, if your child does best when moving through a subject at their own pace, at a time when they choose, on a topic they select, you must take a look at The Khan Academy. It is relatively new, started in 2009, and exisits online only. For a broader description of it, reviews, and the ideas behind it, read this article. This is the sort of thing you could pint your child too and they might just run with it.
Overuse, bad information, bad actors, and bad behavior are common issues. Here are a couple of articles on these topics:
The Children of Cyberspace: Old Fogies by Their 20s, NY Times January 9, 2010
If Your Kinds are Awake, They're Probably Online, NY Times January 20, 2010
Wired Kids, Negligent Parents, "Room for Debate Blog", NY Times, January 28, 2010
As Bullies Go Digital, Parents Play Catch-Up, NY Times, December 4, 2010
It is worth commenting that a couple have studies have shown that, while parents worry about online sexual predators, the far bigger issue in bullying, between kids, online. Here are 3 articles on this and some approaches to handling it:
Studies Reveal Why Kids get Bullied and Rejected, Live Science, February 2, 2010
An online class teaching kindness, from the Puget Sound community School, spring 2010
Lastly, since we get asked, here are a few ideas about parental controls.
FIRST IDEA:....borrrowed from a friend (I assume you know how to look at the "history" of what sites a browser has visited.):
"The thing I wish we had done when the kids were small and first got computers was to lay down the law real clearly: we have visibility into all your computing and we use it. There will be occasional unscheduled inspections of your email, facebook account, etc. This is way harder to impose later when it's time to worry, because it threatens their autonomy just as they are going into the teen and pre-teen years when it's such a huge and emotional issue for all concerned. Get it established early and use it often enough so there's nothing unexpected about it.
You won't need to spend a lot of time looking at logs, just keep the principle clear and your actual use of it obvious but unpredictable. Then I wouldn't even bother with that parental control junk. I don't think it works worth a hoot anyway."
SECOND IDEA, about restricting access to various sites:
Most browsers, like Explorer or AOL, have 'parental controls'. Open the browser and look for or search for parental controls. They can restrict what sites can be visited, time limits, etc. You need to set up your child with a separate account on the pc with only this one browser to use. However these can be easily defeated by a smart kid and most older kids know more about this stuff than parents so it will only work with young children.
THIRD IDEA, about establishing time limits:
Your router has controls that will allow you to set when they work or not. To get to these controls you need the IP address of your router. For Linksys enter 192.168.1.1 in the litte window where you would enter a web address. For Belkin is it 192.168.2.1 It is different for different brands so google, for example "Linksys IP address" or what ever the brand is to find the address. This will establish simple time limits and, combined with the first idea will work fine for older kids.