Are there any mature open source projects that are trying to make personal cloud storage?
I suspect it depends on what "mature" means to you, but owncloud has been around for a little while now, and seems to be updated reasonably regularly. LDAP integration is beta, so it might not be suited to a corporate environment but, for home use, it has been fine for a while (2? 3? years now.)
There is a plug-in for it, which allows you to encrypt the files at rest within the server, but this did not work so well for me, as it never seemed to finish — I don't think I have a big archive, as it is only about 5GB, but they are mostly small documents (and so a lot of them), rather than images or video. Sync only via https can be forced as an option, which is great, and it works fine with self-generated certificates, after the usual "warning — do you want to trust this" dialogue on setup.
Since it uses a flat file structure on the server, no reason you could not rsync that to your chosen off-site storage as a cron job if you wanted, else there is a backup module which might do that for you anyway.