The idea of storing word documents on an external server seems like a convenience, but everyone carries flash drives, so what's the big deal?
But, when you get to the idea of collaborating on something like a spreadsheet with multiple users simultanouesly across the globe, you get my attention. Anyone who's worked anywhere in private industry has probably had to deal with a locked Excel spreadsheet and passed it around the office waiting for someone to close it before it can be opened by someone else. It's a huge pain, and something like Google Docs almost sounds too good to be true.
I would love to use this with other teachers, but there is the added wrinkle of it being online and requiring a login. Not a huge hurdle, but it might seem easier to save something to the school's network and leave it there for others to access.
It could also be a great tool for students entering data from a lab experiment and being able to work on it both individually and together without ever physically meeting. I know that would have been a huge help in some college courses.