Clean up boot partition - Ubuntu

1. Check the current kernel version

$ uname -r

It will shows the list like below:

3.19.0-64-generic

2. Remove the OLD kernels

2.a. List the old kernel

$ sudo dpkg --list 'linux-image*'|awk '{ if ($1=="ii") print $2}'|grep -v `uname -r`

You will get the list of images something like below:
linux-image-3.19.0-59-generic
linux-image-3.19.0-61-generic
linux-image-3.19.0-65-generic
linux-image-extra-3.19.0-58-generic
linux-image-extra-3.19.0-59-generic
linux-image-extra-3.19.0-61-generic

2.b. Now its time to remove old kernel one by one as

$ sudo apt-get purge linux-image-3.19.0-58-generic
$ sudo apt-get purge linux-image-3.19.0-59-generic
$ sudo apt-get purge linux-image-3.19.0-61-generic
$ sudo apt-get purge linux-image-3.19.0-65-generic

When you're done removing the older kernels, you can run this to remove ever packages you won't need anymore:

$ sudo apt-get autoremove