My data set is about 8 TB (my wife is a professional photographer), and it would be too expensive to keep in S3, so I have an "offsite backup system" that is hosted at my in-laws. It's just a RaspberryPi + an 8 TB drive encrypted with LUKS (in case it gets stolen or tampered with).
Every night, the RPi syncs the data from my house with rsnapshot (which is a TimeMachine like tool that uses hard links with rsync over ssh).
Because of how rsnapshot works, I can always go there and look for a file in one of the directories: it looks just like the original hierarchy, and I can just browse the filesystem as I would on the original system.
I also don't have to "trust a 3rd party" that the data is really there. I remember some posts on HN about people who used some backup services successfully... until restore time. I'm always cautious about the magical "set it and forget it" service that is a black box.
The first sync has to be done "on the premises" because of the sheer amount of data to transfer, but then the few daily Gigs of data can easily go over the net while everyone is sleeping.