I think Silverlight is only required when you want to create applications like Flash. These applications are combined into a single executable which are downloaded once on the client machine. They can communicate with the server if they need any data or any functionality which resides on the server. The end user needs to install the Silverlight environment add-on to help run these applications.
Whereas if you create an asp.net application, its code resides and executes on the server itself and hence a simple internet browser can execute it. But the downside is that for user-interactive applications, there need to be separate calls made between the server and client machine when the code requires.
