Funnily enough this was going to be my starting point into writing a C webapp. I felt that by writing a C module directly embedded in an existing web server it would allow me to leverage the request handling. Having already done bugfixes for apache C modules are work it felt the most relevant path to take. The problem I see with it though is you are bound to the webserver you write the module for. Portability would be nice.
(Or more probably since it's 2011, I'd try an nginx module (or lightty), although I have never looked at any of those projects code yet).
Building response stuff in C is pretty high maintenance stuff though.