Starting with vSphere 4.1, the Copy and Paste options are, by default, disabled due to security concerns. Check out this KB Article to enable it : VMware KB: Clipboard Copy and Paste does not work in vSphere Client 4.1 and later
I've done some more research and found the following:
SUES 12 is using open-vmware-tools 9.4 and from what I can tell this version doesn't have clipboard sharing yet. Looks like that came out with version 9.10
So it looks like I'm going to have to wait until SUSE updates their open-vmware-tools package.