Not sure about doing it from C#, but your web host probably has a stats engine built in. Take a look in the control panel for your web hosting and see if there's anything there.
If that's not available, I've heard that Google Analytics is quite good, is free, and only requires a couple of lines of Javascript.
Actually, it appears as if someone's done some work on integrating Google Analytics with Silverlight, take a look at
http://silverlightanalytics.codeplex.com/[
^].
Good luck!