I was recently referred to a great article over on CodeProject showing how to implement client logging in your Silverlight apps. In addition to being very informative (even going into describing the Silverlight code Security Model!) I found it to be a very inspiring article. It is well-written with great visual aids (screenshots, component and flow diagrams... you name it!).
Basically, it all boils down to calling a logging method (ala log4net) in your Silverlight app, which then decides locally (based on a config you've downloaded from the server) whether or not to call the web service on the server with the message. On the web service side, you've got "strategies" defined that determine how to process the messages, usually by delegating to another logging framework such as log4net (as in the example included with the article).
Simple and effective. Just my style! Props to Daniel Vaughn for the implementation and the incredibly coherent article!