There is Tarsnap. While it has licensing restrictions that prevent it from meeting the Free Software or Open Source definitions, the source code is available to

There is Tarsnap. While it has licensing restrictions that prevent it from meeting the Free Software or Open Source definitions, the source code is available to study and build yourself. It's run by Colin Percival (cperciva here on HN, former FreeBSD security officer and designer of scrypt, bsdiff, and other useful tools), who many consider quite trustworthy. Data is stored on Amazon AWS, which you may not like, but since it's all encrypted client side all they can really do is traffic analysis. The big advantage of Tarsnap is that it supports efficient encrypted deduplicated snapshots; it only stores block that have not been stored before, so you can have many versioned backups using much less space than they would otherwise.