Every Ubuntu update installs a new version of the Linux kernel. It keeps the old kernel packages as backup and does not remove them. It does not mark them for autoremove either. Occasionally, I manually remove the old kernel packages keeping the current version and one older version as backup.
Thankfully, I discovered that there is a program that does this exact operation now!
Install the bikeshed package:
$ sudo apt install bikeshed
To remove all old kernel packages except the current one and the next older one:
$ sudo purge-old-kernels
Tried with: Ubuntu 15.10