<p>How do I Configuring DoxyGen to document ActionScript files?</p>

<p>I've included the *.as and *.asi files in doxygen's search pattern, but the classes, functions and variables don't show there.</p>

Instead of doxygen you should use a documentation generator that specifically supports the language. For ActionScript 2, you have a couple choices:
NaturalDocs
(
example
) (free)
ZenDoc
(free)
AS2Doc Pro
(
example
) (commercial)
If you are using ActionScript 3, Adobe includes a free documentation generator along with their open source compiler (the
Flex SDK
), called "
ASDoc
". If you are using
FlashDevelop
, the
latest beta
has a built in GUI for running ASDoc, so you don't have to dirty your hands with the commandline.