mysqlbackup.sh

#!/bin/bash

# This script saves all databases in one file per database
# without the need to enumerate them. It just fetches a list
# of all databases and iterates over this list.

# Config part
user="root";
pass="rootpassword";
backup_path="/var/backups";

# No need to touch here
dbs=`mysql -u$user -p$pass -s -e "show databases;"`;

for db in $dbs
do
    echo "Starting backup of database $db";
    timestamp=`date +"%Y%m%d_%I%M"`;
    filename=${backup_path}/${db}_${timestamp}.sql;
    mysqldump -u$user -p$pass $db > ${filename};
    echo "Compressing backup of $db";
    gzip $filename;
    echo "Backup of database $db finished.";
done

For better human manageability of the backup-files, i would set the filename to ${timestamp}_${db}.sql
So you have all the backups of one day together. Its easier to delete old outdated backups...
Best Regards, Renzo