Benefits of using Silverlight webparts in SharePoint 2010

• Rich, compelling interfaces: Silverlight is capable to produce a UX beyond what’s possible with standard HTML/JS constructs.
• Limit page post backs; Silverlight applications do their processing on the client, eliminating page post backs.
• Silverlight applications offload processing to the client Processing on the client reduces the load on the SharePoint server farm.
• Silverlight isolates processing on the client and creates a self-contained application
  
• Separation of design and code You can use the MVVM pattern to separate the presentation from the processing later.  This makes it easy to change the look and feel of Silverlight applications.
• Common .NET development techniques Silverlight applications are based on the .NET framework which makes it easy for .NET developers to create them.  The client object model may be used to access SharePoint resources from a Silverlight application.
• Overcome Sandbox limitations Silverlight applications may be used to overcome sandboxed limitations such as the ability to call an external service, or use parts of the .NET framework which are not permitted to run in a sandboxed solution.
• Ease of deployment Silverlight applications are very easy to deploy.  Anyone with the ability to upload a document to a document library can deploy a Silverlight application to a SharePoint site.  Additionally, the Silverlight Web Part makes it very easy to place Silverlight applications on SharePoint web pages.

References:

• Silverlight and SharePoint 2010; getting started An excellent overview and tutorial on the three ways to deploy an xap in SharePoint.
• Steve Pietrek is the man who knows everything about the Silverlight/SharePoint marriage.