Not a startup, more like a personal hacking project, but what I am trying to create a cross-platform backup solution that would allow me to do incremental encrypted back up a la Time Machine, for offsite backups. Currently I use duplicity, but the problem with it is I cannot remove arbitrary past back up as it will render backups based on it invalid. That makes it much harder to manage the space on backup disk.
I am aware of the solutions like Tarsnap and Spideroak and I even use some of them, but this is more about very cheap offsite backup of bulk rather infrequently changing data, measure in terabytes, that would be prohibitively expensive to store there.