Would you by any chance be using Google's Chrome browser, Opera, or possibly viewing pages with Flash or Silverlight on it?
You might want to read these:
My guess is that if it is a reputable site that seems to be doing it, and you haven't received anything in Chrome or Opera asking permission to do this, then perhaps it's through Flash (not a lot of sites using Silverlight except perhaps Netflix), and the culprit is ads or some other type of 3rd party provided Flash content.
If you are concerned about security or privacy, you probably should change your Flash privacy settings to either always ask or always deny. You can do that here
is how to change your Silverlight settings.
If you have done all of this and your anti-keylogger software is still complaining about some site trying to access your webcam, the software is probably full of the stinky brown stuff, especially if it goes on to tell you that it blocked it. Some security software likes to scare users by reporting a ton of crap that it "blocks", in an effort to make you think it's doing something useful, so not only will you not think about uninstalling it, you might even think it's worth upgrading to a more expensive version. It's an effective marketing tactic that goes all the way back to software firewalls of the last century.
In any case, it's still a good idea to unplug external webcams when not in use and keep them capped. And not just for privacy and security. Keeping them capped also keeps the lens cleaner.