Flash is one of the many sin’s of the internet if used incorrectly, it both plays a major part in advertisement and even structure of sites in some cases however having a flash dependant site is always ill-advised.
Often many advertisements are still made in flash though utilise the .gif format for the compatibility aspect however this limits quality, 9 times out of 10 the rule is that if it exceeds the quality or reasonable size for download then avoid it.
As well as this the compatibility aspect of flash is one of its major disadvantages, based on the last statistics id seen there where a very low percentage with the .swf flash player plug-in and even less with it enabled and the rough age ranges where that mainly of the younger generation.
Really with flash use of it should depend on your user base and the “usefulness” of the animation or site in that format, by this what extra advantage over say javascript/ajax php/html alternatives.
