WEBROOT was the root of the problem for me.
Right-click tray icon --> View Status --> [Gear icon] by Identity Protection --> Application Protection
The application I wanted to paste into was listed as Deny. I switched it to Allow and it works fine now.
[Kinda mad that Webroot just takes over, classifies a normal app as a problem (Microsoft Visual Studio in my case), and doesn't tell you that it's messing with copy/paste. But at least I know how to deal with it now. Also had this problem with MySQL Workbench.]