You should investigate what's eating up space in your var partition. You can start with something like:
Then try to make some cleanup if possible and see if your server can live like this. Also, if you have a lot of logs you must keep (apache, mail...) make sure you configured log rotate appropriately and eventually that you enabled compression.
If you are still missing space, you then have 2 options:
- resize the var partition.
- move some content of var onto an other partition and maintain the directory structure with symlinks.