From the resource center:The ArcGIS API for Microsoft Silverlight™/WPF™ enables you to create rich internet and desktop applications that utilize the powerful mapping, geocoding, and geoprocessing capabilities provided by ArcGIS Server and Microsoft Virtual Earth™ services. The API is built on the Microsoft Silverlight/WPF platform which is integrated with Visual Studio 2008 and Visual Web Developer Express 2008. The Microsoft Silverlight platform includes a lightweight version of the .NET Framework CLR (CoreCLR) and the Silverlight runtime - all hosted via a browser plug-in.
To use the API you simply download the ArcGIS API for Microsoft Silverlight/WPF libraries and start creating your Silverlight or WPF applications using Visual Studio or Visual Web Developer.
Play around with the Silverlight demo below or see more samples in action!
Download it here: http://resources.esri.com/arcgisserver/apis/silverlight/index.cfm?fa=downloadDisclaimer