I routinely use Remote Desktop (RDP) to connect to my other PCs without having to connect a keyboard & monitor. Until recently I had a problem where I couldn't copy/paste to clipboard whenever I was using Remote Desktop connections.
Various internet searches showed some info but nothing that matched my scenario. Yesterday I checked versions and realised I was still running RDP v5.1 that comes with Windows XP. I upgraded to the latest RDP v6 from Microsoft website (free download) and amazingly the problem has now completely disappeared. Copy & paste works perfectly even when RDP connections are open - result!