I set up an automated backup task which is run FROM a remote computer and which backups everything INTO the remote computer. I know you must be saying “yeah, right, no rocket science so far”, and you are right. Just notice a few things here:
1) The backup runs in a remote computer. That is, the server does not make the backup, instead it is “backed up from outside”. This will work even if the server has a serious problem, in about 50% of the cases or more. In my case, the server had a bad ram module, it was frozen, BUT because the remote access creates an SSH shell and runs as a new user logged into the server, and the base daemons (services) were up, it happened not to interfere with faulty memory space… and it worked even in such conditions.
2) Make separate backups for files and for databases. If all you need is a database recovery, this comes in very handy. In my case, after filesystem backup, I lock all databases, backup them all (it does not take more than 5 seconds in my case), and then unlock them.
3) Make your scrips send you and email whenever the backup has not been done, or finished with some error (in this case, include log files in the email). This is a time saver.
4) Do not keep a compter on just for that task. Simply, dust an old computer and set the bios to wake the box up sometime during the night. Then have a script run on startup where, if current time is between X and Y, then run the backup script, which finishes with a “shutdown” command.

If you are wondering, I use an ancient backup software called Dirvish, which does the trick very well. Of course, it is GNU software. My backup box is a Pentium II with 64Mb RAM, running a base, console-only (no graphical environment), Debian system, which never comes to use more than 16Mb of RAM, and I have turned a Pentium II (= junk) into something useful.

Cheers!