This is an easy-to-use plugin to quickly backup your WordPress database. You may download the backup file, or have it emailed to the address of your choice. By default, the core WordPress tabels are backed up.
You may select additional tables, if any, and choose how you’d like to receive your backup file. This may also be used with the WP-Cron package from Skippy to receive daily backups automatically to your email. Thanks Photomatt
[EDIT] From Dougal: Perl Script to backup and email MySql Databases
I use a perl script to back up my set of databases, and it emails a tarball to my Gmail account for offsite backup.
My database backups have saved my butt a couple of times in the past