Often when you are browsing the internet you come across a great looking site with neat images and great effects. More times than not, it's been made with Adobe Flash.
Naturally, you are going to want something like this. So people will show often show me all these cool effects and full screen sites with big dynamic images.
These things are very neat, but lets get down to what websites are for. Generally they are for presenting information to the public and possibly being able to purchase contact you. That being said, you have to maximize the navigation and accessibility of the site.
A flash site will make the following 2 factors significantly more complicated. They are Search Engine Optimization and Mobile browing.
If you visit a flash site you will notice that usually the url of the site doesn't change as you navigate it. This means you only have one page of content in the search engine spider's eye. However, there may be ways to circumvent this through the use of robot.txt files, but this is going to be a substantial increase in work to develop.
Also it is much more complicated for search engine spiders to determine what text and content is important within the site. That is, if it is able to read the flash site's content at all.
Since the iphone, it is no secret that mobile browsing is on a huge rise. As of yet, there is no adobe flash support in any mobile browser that i am aware of. When phones are able to support flash, that will open a great deal of browsing possibilities, but you cannot code today for tomorrow's capabilities.
I find it highly annoying when sites use flash navigation bars. Then I go to visit the site on my phone and I can't do anything!
Another thing to consider is that often you will have to install flash on computers and some people are not technically gifted enough to perform this action.
Internet Explorer 64-bit does not support flash. So those security nuts out there who like 64-bit browsing will not be able to use it either.
I imagine the time will come when flash is capable of working on everything; However, the internet is still setup to handle HTML primarily and the capabilities of HTML will inevitably be expanded upon.
Final question: Considering Flash is very Application like, why do you not see Google use it when they are trying to expand what you can do in the browser (gmail, google docs, google maps)?