Rated 5 out of 5 stars

Best add-on by far. But if you wish to turn off notifications its an easy process.

Just go to about:config, set the setting extensions.copyshorturl.notifications to:

0: Switches off notifications altogether
1: Always uses a standard notification bar
2: Uses Growl if present, a notification bar otherwise.

This review is for a previous version of the add-on (1.4).