You could always use mysqldump, scp/ssh and a cronjob to automate the backups.
The way I think of it you have a script that
-dumps the database
-copies the dump to the backup server via scp
-calls a script (via ssh) on the backup machine that updates the database from the file that was just scp'ed.
all controlled by crond.
I've heard a bit about replication but I'm not sure if this is what replication is for.