Usability "expert" Jacob Nielsen recently published Flash: 99% Bad, an arcticle that reminds me of Dack's Flash Is Evil article published over a year ago. Dack has also done an informal Usability Test pitting HTML vs Flash. Go and read about the unspeakable horrors of Flash. Then read Kottke's response to the Flash Usability Challenge in which he makes several good points about Flash and its good uses.
In my opinion, there are two types of sites that can work with Flash:
Personal sites - Visitors to a personal site are not as goal oriented as they normally would be (at, say, an e-tailer for example). Flash won't necissarily make a personal site better, I just think its more acceptable on a personal page where I'm not looking to perform any specific tasks. Flash software isn't very cheap either, making it less viable to a personal site developer.
Graphic Design sites - Graphic Designers all but need Flash so that they can show... well, their designs. Flash offers a good compression for the kind of graphics and animation that a Graphic Design site would entail. Again, Flash makes their site less usable, but it is acceptable since it is showcasing what they are selling (graphic design).