Okay, so this forum uses PHP with MySQL... I have access to PHPMyAdmin on a remote server. I have been making periodic back-ups (dumps of the tables) but I'm always afraid that when I need them most, they'll fail on me. There isn't by any chance an easier way to back-up an sql database in linux, right? I have ssh access.

You can go two ways: using the command "mysqldump" which generates a text file of sql commands that would generate your current database. This is what I think you're doing now. The other way is to just copy the database directly. You might want to do this, but I don't know if you'd have access to the database files. Are you afraid that the backup file will not work correctly when restoring? You should try (if you haven't done so) set up some sort of schedule so it backs up the db once in a while.