If you set up this binding:

  bind-key -T copy-mode-vi MouseDragEnd1Pane send -X copy-pipe-no-clear 'xclip -i -selection primary'

(or -T copy-mode, if you use emacs-flavored tmux)

Then you can paste your tmux selections into other programs with middle-click -- I think by default tmux only uses the "clipboard" selection, but middle click pastes the "primary" selection.