A U.S. based shadow network called the ESnet, used by scientists at NASA and the like, is pushing real world, cross-country data speeds up to 91Gbps. That is about 100X faster that Google Fiber, which itself is about 100X faster than typical 'Broadband' speeds to most homes.
Over on Android Authority, I explain a bit about how this network operates, who gets to use it, how it compares to other high-speed networks and more. There is also some great ideas in the comments on what one could use these speeds for. Some intelligent stuff in there, some junk too.