You can, but don't think your html will validate following W3C standards. Not that Firefox uses "Title" instead of "alt", so its wise to have both in as your image attributes.
There isn't really a use for an alt text in other tags as far as i'm concerned, as it is designed specifically as "alternate text" for objects that aren't text and which certain browsers / users can not comprehend without an explanation.
As for Flash, use
SWFObject, it allows to have a div with textual explanation of the flash content for those without flash. And it seems to be ok with Google and SEO.
EDIT: I believe the alt attribute can also be used in the "a" tag when writing links. (at least I do sometimes)
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