Since tmux version 1.5, paste buffers belong to the tmux server and so, are common to all clients.
tslime.vim This is a simple vim script to send portion of text from a vim buffer to a running tmux session. It is based on slime.vim http://technotales.wordpress.com/2007/10/03/like-slime-for-vim/, but use tmux instead of screen. However, compared to tmux, screen doesn't have the notion of panes. So, the script was adapt to take panes into account. If you use version of tmux < 1.3 , you should use the stable branch. The version available in that branch isn't aware of panes so it will paste to pane 0 of the window.