The following is a simple and easy way to get clipboard sharing with Vim working between two Linux installations (specifically a desktop and remote server).
First install xclip on both your local machine and the server:
apt-get install xclip
Installing xclip will bring along some dependencies like x11-common, but don't worry, you don't need to run an X server on the server to get this working.
Next, enable X11 forwarding on the server. Add the following to /etc/ssh/sshd_config:
Then add the following to the server's ~/.vimrc:
vmap "+y :!xclip -f -sel clip map "+p :r!xclip -o -sel clip
This will remap the "+y (copy) and "+p (paste) commands to use xclip.
Now you're done. SSH into the server with ssh -X, fire up vim, and see if it works. If you don't want to type -X every time, you can add ForwardX11 yes to /etc/ssh/ssh_config on your local machine to make it always try to forward X.