Here's an example set of commands used to clean up a Linux boot partition. Of course, replace exact image and header numbers with appropriate version numbers vis-à-vis your machine.
dpkg --list 'linux-image*'
sudo apt-get --purge remove linux-image-3.16.0-41-generic
dpkg --list 'linux-headers**'
sudo apt-get --purge remove linux-headers-3.16.0-41
You can also use df -h to see disk usage before and after.
(Reposted from my tumblr.)