There are ways around the search engine issue. And I actually disagree with most of thatrenowned's comments.
* The saturation level of the flash plugin on the internet is 97% (if you believe Macromedia's statistics). I would not even call that a consideration.
* Having Flash (and someone who knows how to use it) would not really be an issue if you have already created the flash site.

There are many tricks for building dynamic flash sites that can be maintained by simply updating text files. This can actually be easier than updating HTML because no code knowledge is necessary. You can also easily build data driven flash sites with an interface for updates.
* It is true that Flash sites can be larger, but that usually depends on how much audio, images, or movies you have loaded into them. If you load those items at runtime you save yourself a bundle on download times. In other words file (site) sizes are manageable.
* A well developed flash site will not make you watch repeated animations. It is much the same as a well developed site in HTML, it really just depends on the person who designed/implemented the interface.
All that said... I do aggree that in most situations a combination of the two technologies (HTML, Flash) is the more practical way to go... but I for one do not hesitate to create dynamic web sites that are entirely Flash if that meets the design requirement.
Just my two cents.
Wow JT that almost looked like you knew what you were doing!