In doing an investigation as to why FaceTime was not launching (which has been going on since the beta), I came up with this solution to the vexing problem, and here's what you need to do: Go to /Applications, then Right (or Ctrl)-click on FaceTime.app and choose 'Show Package Contents.' Then open the Contents/LaunchAgents folder, and copy the file called com.apple.imagent.plist to your ~/Library/LaunchAgents folder.
There is another file that you need to copy to your ~/Library/LaunchAgents folder as well, but that file on some Macs may or may not be installed. That file is called com.apple.apsd.plist. If that file is not located in ~/Library/LaunchAgents, you may have to download it.
You can do a search for the file on Google or your favorite search engine. After it's downloaded, rename the file com.apple.apsd-ft.plist and put this file in ~/Library/LaunchAgents and launch FaceTime.
If you see your camera light turn on and see your face, just sign in with your Apple ID or MobileMe account and you're all set.
[crarko adds: I haven't tested this one. If anyone has a further explanation of what is going on here, and why the .plist files are not installed in ~/Library/LaunchAgents to begin with, please post it in the comments.]

