I have the feeling that Flash-based ( or Silverlight-based) websites are generally frowned upon, except when you are creating games or multimedia-content rich applications.
Flash is infamous for its poor accessibility.
Keyboard navigation does not usually work, and Flash (up until recently) did not have search engine support.
Flash applications does not work in mobile phones and other portable devices.
Flash is not there in the iPhone!!!
Flash is controlled by a single company (Adobe) and so it is not following any well defined standards for the Internet.
The beauty of Internet lies in the fact that you can always view the source code of any website you are in. This way you can use the same programming/design techniques in your website or you can find security flaws in the web application. This is not possible in Flash. In Flash, source code is closed.
The big question is, why should you use Flash "except when you are creating games or multimedia-content rich applications"?
jtyost2 says, "I would also add that you can't directly link to any content inside of a Flash site, thus breaking one of the major factors that makes the Internet, the Internet, links."
Flash sucks and I refuse to visit Flash-based web sites. Why? Because I can't. Why? Because Adobe is too ignorant to write a plugin for a 64-bit browser.
Flash has its uses. It's good for content, not webpages.
Printing is often poorly supported and the backbutton does not work.
All of the above is true for the wild wild web.
However, for internal business applications, Flash and Silverlight allow the user to have something close to a fully-fledged application in their browser. Accessibility, SEO, and closed source are not very important in an internal application. All that matters is making the user's life easier.
Flash is one more stuff to learn in web development. No thanks! There are just too many already. If I can do my job without it, I don't need it.
Programming is being paid less every day.