Silverlight is no longer allowed on Chrome, for one - there's no way to enable it, period. Additionally, Esri is retiring Silverlight and Flex June 1, 2016 - http://downloads.esri.com/support/product%20life%20cycle/online_gis/ArcGISWebMappingAPIs_PLC.pdf
If your user base employs IE, are happy with the level of functionality currently given by Silverlight, and will never need Esri's help after 2016, you can still use Silverlight - I would just recommend moving away from it as fast as you can.
Silverlight officially dies 10/12/2021, but it is important to note that browser support will likely decrease in the coming years. I can envision a scenario where it is solely supported by IE, under very specific circumstances.
