Couldn't find the simple solution on SO, so thought I would add this here for anyone looking in the future.
My symptom was that I could copy and paste within the IJ editor, but not from the editor to another application or from another app to the editor.
This was on Windows 10 with IntelliJ IDEA 14.1.6.
My solution (thanks to a similar issue reported with Android Studio) was to run IntelliJ as an admin.
Steps to always run IntelliJ in admin mode: