You have a need for great looking and interactive web applications (that are not Ajax, jQuery, etc.).
You want to utilize your current programming language (VB.NET, C#, etc) skills.
You want your "web app" to be available out-of-the browser.
There are other reasons - have a read: Top 10 Reasons to Use Silverlight. There can be a significant ramp you would need to make, but once made, you may prefer SL for certain things over ASP.NET and even in some cases, not really have option available to you in ASP.NET, like, for example, perspective transforms of images that can be animated from user interactively.
Thanks & Regards,