Just one of the 10 sites configured on my Local IIS was giving this error, so I had a feeling that it wasn't anything from the other answers that were machine-wide things, like Turning Windows Features On or Off, or running VS2015 as admin (the other 9 sites worked ok, in the same VS).
The specific error for me was:
Unable to start debugging on the webserver. Operation not supported. Unknown error:0x80004005
The problem turned out to be the web config having a URL Rewrite rule to rewrite HTTP -> HTTPS. Commenting this out resolved the problem
TL;DR - try disabling all your web.config URL rewrite rules, if you have them (then add them back in gradually, if it helps)