I don't want to start a war, but I feel that there are very clear criteria for the use of Flash.  There are other times when the call on whether to use it is or is not as clear, but these are the times when I known I need to use it.

Graphic - intensive interfaces where ther is a great deal of animation and /or interactivity,
Places where animations are needed for explanation of concepts or for the exposition of content.
Cases in which you wish to pass variables to/from Java/Javascript objects regarding th control of animations.
(This is my main use of Flash)
Graphically-based animation with low file size (this is very different from Real or Animated Gif)
Sites with many interlocking animated sections.
Interface structures that do not fit well withing HTML paradigms.

I usually get very tense when I see the "Gabocorp opening screen" sort of opener.
The only people who have impressed me with their opener is:
http://www.idgruppe.com

Being innovative is problematic at best.
I know I'm lousy at it most of the time, but you have to try.
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