Copying text outside of Vim with set mouse=a enabled

Use ", +, y after making a visual selection. You shouldn’t be using the terminal’s copy command anyway, because that copies what the terminal sees instead of the actual content. Here is what this does:

• ",+ tells Vim to use the register named + for the next delete, yank or put. The register named + is a special register, it is the X11 clipboard register. (On other systems, you would use * instead, I think, see :help clipboard and :help x11-selection)
• y is the yank command, which tells Vim to put the selection in the register named previously.

You could map it like this:

:vmap <C-C> "+y

And then highlight something with the mouse and press Control-C to copy it.

This feature only works when Vim has been compiled with the +xterm_clipboard option. Run vim --version to find out if it has.

Press shift while selecting with the mouse. This will make mouse selection behave as if mouse=a was not enabled.

Note: this trick also applies to "middle button paste": if you want to paste in vim text that was selected outside, press shift while clicking the middle button. Just make sure that insert mode is activated when you do that (you may also want to :set paste to avoid unexpected effects).

OS X (mac): hold alt/option while selecting (source)