5 Free Linux Backup Solutions

rsync
There are tons of Linux users and administrators out there who have customized rsync scripts to handle incremental backups automatically on a daily, weekly, or monthly schedule. From the manual, rsync is described as a program that behaves in much the same way that rcp does, but has many more options and uses the rsync remote-update

protocol to greatly speed up file transfers when the destination file is being updated. The rsync remote-update protocol allows rsync to transfer just the differences between two sets of files across the network connection, using an efficient checksum-search algorithm described in the technical report that accompanies this package.

Here are a few resources for learning how to set up a Linux backup solution using rsync:

http://www.mikerubel.org/computers/rsync_snapshots/

http://finmath.uchicago.edu/~wilder/Security/rsync/

http://www.sanitarium.net/golug/rsync_backups.html

mondorescue

Mondorescue backs up your GNU/Linux server or workstation to tape, CD-R, CD-RW, DVD-R[W], DVD+R[W], NFS or hard disk partition. In the event of catastrophic data loss, you will be able to restore all of your data [or as much as you want], from bare metal if necessary. Personally, I like using Mondorescue to create DVD disk images of my system periodically. Upon initial installation and configuration of my Linux or Windows machine, I create a DVD disk image with Mondo so that if anything ever gets screwed up, I can pop in the DVD disk and restore back to my original configuration. The mondorescue team is great and the lead developers of the project are very active on the public mailing list offering help to normal users whenever needed.
Simple Backup Suite (Ubuntu, Gnome)

If you’re running Ubuntu Linux and are looking for a quick backup solution, I suggest checking out Simple Backup Suite, or sbackup for short. Simple Backup Suite is a simple backup solution intended for desktop use. It can backup any subset of files and directories. Exclusions can be defined by regular expressions. A maximum individual file size limit can be defined. Backups may be saved to any local and remote directories that are supported by gnome-vfs. There is a Gnome GUI interface for configuration and restore.
Amanda

AMANDA, the Advanced Maryland Automatic Network Disk Archiver, is a backup system that allows the administrator to set up a single master backup server to back up multiple hosts over network to tape drives/changers or disks or optical media. Amanda uses native dump and/or GNU tar facilities and can back up a large number of workstations running multiple versions of Unix. Amanda uses Samba or Cygwin to back up Microsoft Windows desktops and servers.
Bacula

Bacula is a set of computer programs that permits the system administrator to manage backup, recovery, and verification of computer data across a network of computers of different kinds. Bacula can also run entirely upon a single computer and can backup to various types of media, including tape and disk. In technical terms, it is a network Client/Server based backup program. Bacula is relatively easy to use and efficient, while offering many advanced storage management features that make it easy to find and recover lost or damaged files. Due to its modular design, Bacula is scalable from small single computer systems to systems consisting of hundreds of computers located over a large network.