exporting from phpmyadmin is good but personally i use the cron job feature. it emails me a copy of my entire database every day. i use gmail so there's loads of space for it. you can set the job to run at any time of day and a varying intervals, it doesn't have to be every day.
just go to cron job, choose standard and then choose your time of day and how often. put in an email address to receive it.
i used the following command, obviously replacing the caps with my own details. so i get a massive load mysql commands that i can run to restore my db structure and all my data.
mysqldump -u DBUSERNAME --password=DBPASSWORD DBNAME
you could run a php file instead and make things a lot more tidy. like getting it to email you your db as an attachment.
you could use a command like this...
wget -q
http://yourdomain.com/phpmysqlautobackup/run.php
obviously it doesn't matter where the php file is located. it should be pretty easy to find a ready made script somewhere.