You can uninstall or removes an installed awn-applets-common package itself from Ubuntu 12.04 LTS (Precise Pangolin) through the terminal,
$ sudo apt-get remove awn-applets-common
If you would like to remove awn-applets-common and it's dependent packages which are no longer needed from Ubuntu,
$ sudo apt-get remove --auto-remove awn-applets-common
If you use with purge options to awn-applets-common package all the configuration and dependent packages will be removed.
$ sudo apt-get purge awn-applets-common
If you use purge options along with auto remove, will be removed everything regarding the package, It's really useful when you want to reinstall again.
$ sudo apt-get purge --auto-remove awn-applets-common