Meet Alfred. Alfred is a Debian user. He has a laptop with Debian and a desktop environment running on it. Alfred does a lot of impotant things on his computer: his hobby is to photograph his cat, and also he works for a non-governmental organisation that investigates and reports on human rights violations. His job involves a lot of travel to many parts of the world, and he needs to handle a lot of very sensitive information. His laptop uses full-disk encryption, and it's generally speaking very well secured against the various security threats that are due to his job.
He is worried about losing important data. He's not too worried that the sensitive information he has will leak if his laptop is stolen, but it might be impossible to re-create the data if the laptop is gone. If he interviews a whistleblower for a slave-trading corporation, and his laptop is stolen after that, it might be impossible to ever meet with the whistleblower again.
Alfred wants backups of his data. He gets a USB thumb drive, and plugs it in. The laptop has never seen the drive before, so it asks Alfred if the drive should be used for backups. Alfred says yes.
The laptop formats the thumb drive, again with full-disk encryption, and then runs a backup. The backup automatically picks up all the files from Alfred's home directory, and some system confguration files that may be necessary as well. (Read: /home and /etc.) Files that are usually not very precious, such as web browser caches, are automatically excluded.
Later, when Alfred wants to update the backup, he plugs in the same drive again. The system recognises the drive, and runs the backup. While the backup is running, Alfred has an indicator in his desktop status bar. If Alfred leaves the drive plugged in, and changes anything in his home directory, that gets immediately backed up to the backup drive. Until the changes have been backed up, the indicator stays on Alfred's status bar.
This isn't good enough, however. Alfred needs to carry the USB drive with him, and if he's mugged, he might lose both the laptop and the backup drive. Therefore, the system administrator at Alfred's NGO, Janet, sets up an account on an online backup server, and e-mails Alfred a configuration file, which Alfred drops into the backup system's configuration tool.
From then on, whenever Alfred's laptop is online, and can see the backup server (identified by an SSH host key), any changes Alfred makes are backed up as soon as possible. For the next interview, as soon as the interview is finished and Alfred closes the laptop lid to suspend it, the backup has already finished, both to the online server and the USB thumb drive.
Alfred is now happy, and no longer fears for the safety of his data.
Janet, however, is still a little worried, because the online backup server is an attractive target for attacks. She asks Alfred to configure the backup service on the laptop to encrypt and digitally sign the backups, and sends the master backup public key with the request. Janet keeps the corresponding private key in a secure location.
Alfred goes into the configuration dialog, ticks the right box, and drops in the server public key. The backup software generates a new public key for the laptop to use for encrypting the backups, and Alfred e-mails that to Janet, using PGP encrypted and signed e-mail. He also puts the laptop backup encryption keys on a couple of USB thumb drives, which he stores in safe places (in his sock drawer and coffee jar, but don't tell anyone that).
Alfred's online backups are now encrypted with public keys so that both Alfred and Janet can decrypt them, but only they can do that. The backups are digitally signed so that if the server is hacked, the backups can't be altered without it being detectable.
Some time passes.
Alfred needs to go to speak to the general assembly of the Cat Conference, about how awesome his cat is. This requires him to travel to the US, and he's worried that the US authorities will confiscate his laptop and try to get at his work files that way. He deletes all his work files, ssh keys, and other files that aren't necessary to show his cat pictures at the conference.
The conference goes fine, and when Alfred comes back home, he gets the USB thumb drive that contains his backup encryption key. He plugs it in, tells the backup configuration software to import it. Alfred can then open his backups on the online backup server in his file browser, and can restore back his files by copying them with drag and drop.
However, the next day Alfred's cat, upset at how much he travels, pees on the laptop. It is ruined. Everything is lost.
Alfred gets a new laptop from Janet, and installs Debian on it. During installation, Alfred gives the installer the USB backup drive, and the installer restores all of Alfred's own files, and also restores system configuration. After a little while, Alfred has a newly installed laptop with all his usual software and all of his files.
This is a summary of a vision for backups being a service in a default Debian install in the future. It is currently just a vision, and nobody is currently working on making it reality. Would you like to work on this for the release after jessie?
(No cats were harmed in the production of this vision.)