I did find a few Linux backup suites, but unlike Windows, most things in Linux are done with basic tools and some scripts to automate the task.
In the case of backups, there are a few tools you can use. Rsync will keep directory trees up to date, so if you just want to keep a mirror of your current system at all times, that's the easiest way. If you want to have daily diffs (e.g. so you can go back before something got deleted), then rdiff-backup may be a better solution. If you want to get fancy, you can wrap these in scripts to compress the diffs, name them, etc.
Finally, these programs don't run all the time in the background, they just do their job once when executed. If you want them to run periodically, you'll want to use the cron. Cron is basically a scheduler that periodically runs programs at given intervals. Look into cron and the crontab to see how to set this up.
Alternatively, if you want something more powerful and that requires less scripting, look into AMANDA. The company I work for is currently using rdiff-backup, but is planning to move to AMANDA because of the extra abilities it has (such as backing up different sources to different drives).
Just remember not to backup to the SD card -- it's only good for a few thousand writes. You should really use an external HDD for anything that needs to be non-volatile, but will change often.