<p>I have written a simple HTTP Proxy server in C# that I would like to integration/functional test.  Is there a product already created that I could use to do this?  If not, what is the best way to write my own tests for this (I already have unit tests)?</p>

To test the integration by delivering a webpage you could try one of the following:
Selenium
WaTiN
Watir
You can run Watin tests directly from xUnit in C# too - we do this for our applications. I also believe it is possible to dynamically set the proxy settings in the browser for Watin (and probably the others too).
Alternatively to make HTTP requests to a given address try
JMeter
.