I've spoken before about ZUI (Zero User Interface) and how often it's the right interface.
One important system that often has too complex a UI is backup. Because of that, backups often don't get done. In particular offsite backups, which are the only way to deal with fire and similar catastrophe.
Here's a rough design for a ZUI offsite backup. The only UI at a basic level is just installing and enabling it -- and choosing a good password (that's not quite zero UI but it's pretty limited.)