I have a RHEL 6 Desktop with a windows KVM. How could I get the clipboard working, just as there is a solution in VirtualBox to share the clipboard between host and guest?
As already mentioned by @gertvdijk, SPICE is KVM's own way to address that.
Otherwise, a more generic solution that works equally well for any type of virtual and real machine is to use remote desktop or VNC to connect to the machine itself.
If you're not using SPICE, you're using VNC already anyway. However, in that case, the VNC server is provided by the host (which serves the video memory, keyboard and mouse of the Guest, but has no access to the Guest's clipboard which is something internal to the desktop environment inside the Guest).
By moving the VNC server to the Guest, you put it in a place where it has access to the clipboard.
Remote Desktop has a few other advantage over VNC (like file, device and sound sharing).