I went to update my Ubuntu machine today and found out there wasn't enough space on /boot to perform the update. You can remove older kernels to free up space:

// Check which kernel you're using
$ uname -r

// List all installed kernels
# dpkg --list 'linux-image*'

// Remove the kernel (I recommend the oldest [kernel with the smallest number])
# apt-get remove linux-image-VERSION

Source: https://askubuntu.com/questions/345588/what-is-the-safest-way-to-clean-up-boot-partition