My /var directory is only 9.7gb in size - it has accumulated more data than the partition size currently.

Is there a way to safely increase partition size without having to back up the data?

If not, what method of backing up would you suggest? Having to transfer the 800 gb of data over the net to my clientside (non-server) would take days, if not weeks, using my DSL connection! Would copying the partition to another partition work as a backup? (But, I imagine if something goes wrong with the re-partition, the entire hard drive would fail?)

Why not clean your /var partition up? Im sure you dont need everything there. You can also move some high capacity directorys off of /var to a larger partition and then create a symlink.

But i would really reccomend just cleaning the partition up...

I am not a fan of the default cPanel partition scheme for this reason. Typically the problem is your databases or your domain logs. As Gary said, you should definitely consider cleaning up your logs.

If the problem is your mysql databases, then you may need to do something a little different. Such as storing the databases on a different partition, then using the bind flag with mount to avoid breaking any existing config.

Another idea would be to create a filesystem within a file on another partition, and mount it in place of /var/lib/mysql.

If you don't feel comfortable doing this yourself, you can always put in a request to Advanced/Professional Services, or hire a third party.

I guess you need to check this : http://www.eth0.us/mysql-dir