What's the best backup solution for Linux that can completely restore the entire filesystem to a blank harddrive (including partitioning) after an old harddrive dies?

I'm currently running a few Ubuntu machines, some with RAID-1 and others without RAID (mostly laptops). I'd like to implement a backup solution that can take incremental snapshots of the entire filesystem, so that if I were to replace all the harddrives in a machine, I could use the backup to restore a perfect copy of the previous filesystem.

Unfortunately, nearly all the backup solutions I've found seem to be glorified rsync scripts, which only backup some files, and have no easy way to restore once the entire filesystem is gone. Some of the more complicated solutions, like Bacula, might do what I need, but require a complicated server/client setup and are notoriously difficult to maintain.

I've heard that Apple's TimeMachine utility has this ability, and I've had similar success taking differential disk images with Acronis True Image on Windows, but of course neither of these work on Linux. Is there anything comparable for Ubuntu?