Public Websites done completely with Flash or Silverlight can be very eye-catching and used in the right spots can achieve way more than you can ever achieve with HTML. But beware because:
It does not work on an iPhone or iPad
Flash/Silverlight can be slow loading, especially if the visitor is not using a fast Internet connection. If your website doesn't load within 5 seconds, they're gone. (There are techniques to overcome this)
It is bad for search engine rankings as there is no content for search engine spiders to crawl through. (There are techniques to overcome this)
Navigation via the back button (and Browser History). (There are techniques to overcome this)
Accessibility
Often seen with busy designs that turn off or distract visitors. Look at the biggest ecommerce sites and you notice that none of them are Flash websites
In many cases it unnecessarily creates page bloat
You can *almost* get the same effects and functionality using jQuery, but faster and lighter
You get an inconsistent UI if you use it for controls such as text boxes
Flash and Silverlight do not support CSS, so you need to follow unfamilar concepts for re-skinning
Finally, and saddest of all, when Flash/Silverlight is used, it is normally over used.
Footnote #1: It is clear that Flash has been quite successful in the past - the penetration of its run time is 99% on PCs, however because of the fact iPhone and iPad don’t run it and the growth of HTML 5, Flash is now considered an old technology.
Footnote #2: The development of Silverlight has been discontinued as of 2012 due to the poor acceptance of Silverlight and restrictions Microsoft imposed on its utility.