Your backup solution should offer a way to exclude folders from its backup catalog.
Exclude var/session/, var/tmp/, var/cache/, media/tmp/ and media/catalog/product/cache/
cPanel backup solutions might have the file that contains the exclusions owned by root, see your hosting provider for help adding the exclusions.
Preventing session files from being created during your backup would require a Error 503 suspension of system activity by putting your system in maintenance mode during the backup operation. 1.4.x.x versions can be put into maintenance mode by creating a file called maintenance.flag in the Magento root directory.
Excluding directories from backup will allow you to back up at any time without shutting down your site. Going into maintenance mode means your site is down during the duration of the backup, not a very good solution on a busy site unless you can automate the whole thing to happen around 11:00 pm store local time when it won’t interfere with Magento’s scheduled maintenance.