It's a huge topic and you can read articles all day on Flash-vs-Silverlight-vs-AJAX.
I use Silverlight and was completely over the moon when it was released due to the ability to employ the CLR in browser based applications. Javascript/DHTML development drives me nuts and for me Silverlight was my way to escape its clutches. As far as Flash goes my very brief foray into it found ActionScript to be more painful than Javascript but that was years ago and things have undoubtedly improved since then.
Basically if you're using .Net for your back end then it makes perfect sense to use Silverlight for the front end. It means you only have one development environment and language to deal with and where appropriate you can reuse a lot of your back end code on the client.
In practice it's not quite that easy and my experience has been that there is a lot of resistance in user land towards Silverlight. The main bone of contention is generally that the cross browser and operating system support is not good enough. Users that employ Opera or use Linux or PowerPC Macs can't use Silverlight (Moonlight isn't there yet). Those users are generally vocal ones.
If you know all your users will be on IE/Firefox on Windows/Mac Intels or you have a compelling application that users will change their set ups for then Silverlight is almost certainly your best option. If you have an application that you want to hit a wide range or disparate users you may need to weigh up the options a bit more.