This is a trick that works on a Linux system, as most servers are hosted using Linux. So, you would have to figure out how to change it if you are using Windows (sorry).
What are we going to do?
We will just create a simple bash script that will backup all databases, and we will create a cron job to do it for us on automatic intervals.
The Bash Script
You may first ask me, why do this in a bash script? Why not put it straight into a cronjob? Well, I'm doing it just to make it easier if you want to run other commands, or do one file per database. So, here's the script:
#/bin/sh
mysqldump -h localhost -u mikesir87 -pPASSWORD --all-databases > database.sql
gzip database.sql
mv database.sql.gz BACKUPS/`date +mysql-BACKUP.sql-%y-%m-%d.gz`
The first command, mysqldump, does a simple dump on the database. Since we give it the --all-databases flag, it grabs all databases that user has access to. The -h flag is for the host, which will probably be localhost. The -u flag is the username for the connection and the -p flag is for the user's password. Note that there is space between the flag and the password. If you're not familiar with Unix command lines, the > is what is called an IO Redirect.