I just installed Windows 8.1 64-bit. This is weird because I've used Win 8.1 before and don't remember ever having to give my webcam permissions to specific apps.

However, when I launch Windows Essentials - Movie Maker, I see my webcam in the OPTIONS window, but no stream, just a black window.

I had the same issue with Skype. 

I found a support article showing how to get to the webcam permissions screen (in Metro: win+c, type webcam, click on webcam privacy settings. I enables Skype and all is well in Skype.

Essentials Movie Maker is not listed and there is not way to "search for other apps" or the like.

I just started using Movie Maker on my Win 7 laptop and it just worked, even with the same USB webcam and the built in webcam.

Any help or direction is greatly appreciated.