Your /boot partition is for boot related files and holds the kernels installed on your system. If you haven't removed any older kernels, your /boot partition will likely fill to capacity.

It's safe to remove old kernels, but first determine which kernel your system is currently using:

uname -r

Then determine what other kernels are on your system:

dpkg -l | grep linux-image-2

You must keep your current kernel and should probably retain one or two of the most recent kernels and remove the rest.

Use the following command to remove a kernel image:

sudo aptitude purge linux-image-2.6.32-30-server

Once you're done removing old images, update grub:

sudo update-grub