The Raspberry Pi was designed as a cheap low cost computer for education. Could it be also good as a low power server dedicated to one app (as Richard has it, a "thin cloud")? It's so cheap you could run two (one primary and one backup at different locations). No need for a datacenter, no need for a hosted service! Begone "tyranny of the cloud" and "tyranny of the hosted service" ?
My guess is the Raspberry Pi is too slow and my internet connection is too slow but it would work for a family webapp only used by two dozen folks! But in the future I don't see why it wouldn't be viable with a better internet connection and faster raspberry pis!
I am going to try this out when my Raspberry Pi arrves later this summer. I am thinking of running Open Photo (a private instance) for family stuff.
The other thing thing I am thinking of doing is using multiple Raspberry Pis to run cool server web app tech, e.g. 1 for clojure, 1 for node.js, 1 for haskell, 1 for racket, 1 for whatever is the common lisp flavour du jour :-) etc
And heck if i have spare time, I'll use multiple Raspberry Pis like D'Arcy, Dave Winer and Tantek; to reclaim my stuff and put it in my walled garden first :-) before I copy it to other walled gardens like Pinterest, twitter, flickr etc