Ubuntu does not remove kernels when they install a new one, however the /boot partition is usually relatively small. So after only a few kernel upgrades, you can get No Space Left On Device errors when trying to upgrade. Then you can either remove them manually, or use this one liner to automatically remove them all.

export KERNEL="$(uname -r | grep -Po '([0-9\.\-]*[0-9])?')"; dpkg --get-selections | grep -E "linux-(header|image).*" | grep -iw install | sort | grep -v "$KERNEL" | grep -v "lts" | sed 's/install//g' | xargs dpkg -P

Here's the command by command explanation:

export KERNEL="$(uname -r | grep -Po '([0-9\.\-]*[0-9])?')"

The first portion sets the current kernel number in a variable KERNEL. It only takes the number, and greps out any additions like -generic or -server.

dpkg --get-selections 

The second portion first prints out all available packages.

grep -E "linux-(header|image).*"

The third portion greps for all packages with either linux-header or linux-image in the name.

grep -iw install

The fourth portion greps out only installed packages.

sort

The fifth portion sorts the output.

grep -v "$KERNEL" | grep -v "lts"

The sixth portion filters out the current kernel and the LTS kernel package. Removing those will cause problems.

sed 's/install//g'

The seventh part strips off the install part.

xargs dpkg -P

The last part actually removes the packages. xargs send all the package names to dpkg. Then dpkg -P purges the packages. That means, removing them and removing their configs.