It is impossible to paste text from the clipboard into text fields in Unity editor. Shortcut combinations does nothing and right-click context menu does not have a "paste" option.

Resolution:
Webroot security software is blocking Unity's access to the clipboard.

Solution provided by the user:
I worked around this by going into the advanced settings in Webroot and unchecking the "Silently and automatically block untrusted access to user data" option under "Shields". Then when I tried to copy/paste in Unity, Webroot popped up a warning and I told it to always allow.

This issue was also discussed in the forum: http://forum.unity3d.com/threads/215181-Windows-Can-t-Paste-in-Editor?p=1441627