rsnapshot is what you are looking for—it gives all the functionality of Apple's Time Machine on Linux systems, except for the GUI for browsing. It creates snapshot backups using the power of hard links & rsync(1) so that it only has to copy newly created or changed files.
While rsnapshot doesn't provide any facility for viewing the backups, it stores them as normal directories, so you can view them in any file manager. The backups folder for my system looks like this:
caligula:/mnt/backup/rsnapshot$ ls -lt
total 48
drwxr-xr-x 3 root root 4096 2010-11-09 05:51 daily.0
drwxr-xr-x 3 root root 4096 2010-11-08 05:51 daily.1
drwxr-xr-x 3 root root 4096 2010-11-07 05:50 daily.2
drwxr-xr-x 3 root root 4096 2010-11-06 05:51 daily.3
drwxr-xr-x 3 root root 4096 2010-11-05 05:51 daily.4
drwxr-xr-x 3 root root 4096 2010-11-04 05:51 daily.5
drwxr-xr-x 3 root root 4096 2010-11-03 05:51 daily.6
drwxr-xr-x 3 root root 4096 2010-10-31 05:50 weekly.0
drwxr-xr-x 3 root root 4096 2010-10-24 05:50 weekly.1
drwxr-xr-x 3 root root 4096 2010-10-17 05:50 weekly.2
drwxr-xr-x 3 root root 4096 2010-10-10 05:50 weekly.3
drwxr-xr-x 3 root root 4096 2010-10-03 08:50 monthly.0