Sounds like it's getting time to install a top-notch anti-spyware program and use it regularly. At this rate, it won't be long before the Watchtower Society starts installing spyware on people's computers to report to Brother Hounder if the user visits a questionable web site or attempts to use independent sources for research.
There are legitimate dangers with the Internet. Predators can be a threat, but to be sexually molested requires an actual physical meeting (which cannot happen directly through the internet). Sexually explicit messages, porn sites, and unapproved music (that is, which is too mature for the child) should be appropriately censored--it's the parent's job to determine what is appropriate and what is not. Obviously, precautions need to be taken to make sure a teenager doesn't mess up your computer with a bad program (many music swapping programs and games carry a payload of spyware). And you do not want your child to order tens of thousands of dollars worth of items without your knowledge or approval.
However, these things aside, children need to be allowed to grow up. If they are kept at Grade 1 forever or everything they do is censored, they are going to regret it, and might just ruin your computer on purpose out of vengeance. I recommend age-appropriate software from a worldly source (you might have to pay for it, but I would rather pay $30 to Microsoft than donate $??? to the Worldwide Pedophile Defense Fund). Some programs are incorporated on your ISP--using them helps. And, a quick check on the history to weed out those seedy sites could be in order.
Above all, any physical meeting of anyone they meet online has to be supervised by the parent. That way, you know you will not be getting into a sticky situation. Of course, you should never allow the child to post sensitive information (identity theft is the risk), but that is sensible for anyone. That leaves the most common thing a computer is good for: research, entertainment, and exchange of ideas. There is nothing wrong with visits to apostate Web sites or independent religious sites. Most, if not all, apostate web sites are clean and safe.
