Backups - How to

I'm now running my main box on Linux more than on Windows. My daily backups seem problematic, though. I have a Travan-5 tape drive that I use for backup. Every week, I backup the entire system to tape. On the other days, I backup everything that changed since the last full backup. I have this set to run (Windows) unattended at midnight, I just change tapes. Tapes are rotated, giving me the ability to get files back at any day over the last month. What can be used to accomplish this on Linux? Backup is a critical operation; I firmly believe that those who don't follow good backup procedures deserve what is inevitably going to happen.