I've been working on Silverlight recently, and have to say that I consider Silverlight to be only for business. (excluding Silverlight for Windows Phone, which is another kettle of fish)
I am aware of a locally based, national retailing company who have their online presence - comprising their online store to which they hope to drive a large portion of their business - completely written in Silverlight. They think it's great! It does look fairly good, and is better than a Flash site in my opinion, but they are missing the elephant in the room: the Silverlight install base is dismal. As more people upgrade to Windows 7 / Windows 8, and IE8 and above, then the install base will increase - but for the guy at home still running XP or Vista and IE7, why would you install some program just so you can view one website?
I think using Silverlight on your external website is a significant fail. It won't run on mobile devices, and won't run on a huge proportion of desktops and laptops. It's like advertising in a foreign language.
The opposite is true in business. Users don't pick and choose which browser they use - it's typically determined by the business. Everyone uses the same software. You can roll out Silverlight to the entire business. At the same time, business loves intranet (go figure) and adore Sharepoint and various other 'online collaboration tools'.
So where does Silverlight fit in? It's a no brainer. Silverlight provides a much better user experience (in terms of looking nice) than ASP.NET WebForms, and isquicker to develop with than ASP.NET MVC. Admittedly you can do amazing things with web technologies these days, but .NET has always been about balancing the end product with speed of development. Silverlight is WPF that can run in your browser. That has a huge business use.