When we click "share" , there is a popup:
In the popup, I suggest we have a Copy button beside the textbox (and near to "share" so as to minimize mouse movement) to make it easier to copy links to the clipboard. After all, that's what the user is most likely to do next after clicking "share".
It might look like Bitly's "Copy" button:
or Github's "Copy the full SHA" button:
Ctrl+C
.bit.ly
. I'm not too sure if they'd like that for Stack Exchange, is what I'm saying :)