A nice piece of set-it-up-and-forget-it remote backup software is rsnapshot.
Since you are using mysql databases I would combine a local mysqldump (easier to recover from then binary database files) with rsnapshot for frequent full system backups. Don't let "full system backup" scare you, with rsnapshot only the first backup will take a lot of time since all files will need to be transferred from the database server to your backup destination. All subsequent backups only transmit new or changed data. Another nice feature of rsnapshot is that it heavily uses hard-links. This makes each snapshot a full and complete copy of the backed up server while keeping total disk utilization for all snapshots very small (size of 1 full backup plus the sum of all new and changed files).
For this suggestion:
1.) run rsyncd on the database server (locked down to only be accessible from the backup server, run as root, no chroot to allow backup of files with restricted access, read-only mode for added security since that is all that is needed for backup purposes
), ideally start it automatically on boot (e.g. init.d).
2.) periodically run mysqldump on the database server (e.g. from cron so that nobody forgets it). It is fine if it always backs up to the same destination on the local disk.
3.) run rsnapshot on the backup server to backup the entire database server (use daily, weekly and monthly cron jobs as desired).Add 'exclude' directives to rsnapshot.conf for virtual filesystems (/dev, /proc, /sys) or anything you really don't want to back up. I also added '--bwlimit=...' to the rsync arguments inside rsnapshot.conf which reduces the impact of backups taken on always up production servers.
Edit: before I get a lot of flak for the "forget-it" part, I specially mean the low maintenance aspect of rsnapshot once it is configured. It doesn't hurt to periodically check rsnapshot.log to see that everything is going smooth just like many other logfiles ought to be periodically reviewed (before warnings turn into fatal errors).
Edit: some additional details added in italic.--
Got some spare cpu cycles ? Join Team Helix or Team Starfire!