I am a network engineer and have had routine access to 100 Mbps and multi-gigabit Internet connections for years. I honestly have no idea what home (or even business) users are going to do with gigabit connections -- including HD video, which is only 15 Mbps. Even with a building full of senior software engineers, it's hard to break 30 Mbps except for 1-2 minute peaks. Even when everybody is streaming media, Pandora only takes about 256kbps, Netflix takes a few Mbps, etc.
With existing tech? Probably not a whole lot. I think that once more people have faster connections we'll start seeing new tech to take advantage of it.