Hey Josh,
I'm a web developer, so I know about dealing with these hosting companies. If your web host does not make (at least) weekly backups of your site (including SQL databases) you should drop them and find a new host that does. I've had client's websites get taken down by hackers before, and my host was able to roll back to the Sunday before and fix everything within a couple of hours...
If you are backing up your files yourself, there is an option in Cpanel under "Backups" that allows you to select a specific SQL database that you can backup and download easily. It should download for you a zipped file containing a .sql file, which is the contents of your SQL database.
See attached screenshot.
http://www.herbertfilby.com/images/cpanelbackups.jpg
Hope this helps!