I currently have a computer serving up web pages from my home computer, but realistically for the traffic it gets it is consuming far too much power. This is where the Raspberry Pi would come in:
I imagine having a board powered by solar power (and batteries), running an small web server (httpd), also capable of running php. This would be connected to the local network either via wi-fi or fixed ethernet. This would act as the primary server and would wake the main server (via WoL), only for certain sections of the site or if the load reaches a certain threshold.
In fact, I really think a solar powered kit (pre-built or easy to assemble) would be a really useful accessory to the Rasberry Pi.
The setup could probably be made to switch to a mains supply if the battery is below a certain charge and a mains current is detected.