I'm having some troubles because the partition in which /boot is allocated in my server is full, so I can install neither new linux images nor upgrades.
Here is the server's file system usage information:
$ df -Th
Filesystem Type Size Used Avail Use% Mounted on
/dev/mapper/PCM-root ext4 442G 83G 337G 20% /
udev devtmpfs 7.9G 4.0K 7.9G 1% /dev
tmpfs tmpfs 3.2G 320K 3.2G 1% /run
none tmpfs 5.0M 0 5.0M 0% /run/lock
none tmpfs 7.9G 0 7.9G 0% /run/shm
/dev/sda1 ext2 228M 225M 0 100% /boot
The specific question is how I can manage to solve this issue without re-installing the system (that is what I'm gonna do if everything else fails)?

dpkg -l | grep linux-image. Any withiiin the left column are currently installed. Do note that at least one of those entries is going to be a meta-package (such aslinux-imageorlinux-image-server) – Powerlord Dec 27 '12 at 14:55