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This sounds like a book that I've never read, but have heard about: My Name Is Red by Orhan Pamuk.
Is it this? I just googled Audio Book Geena Davis, since this is pretty much all you gave us to go on.
DoodlesIt wasn't that (this was a single story). I believe it was for elementary-school-age children. I don't remember any other narrators or even what the story was about (though I'm pretty sure it was set in some sort of storybook kingdom), and I don't remember the year, but I know I would've heard it around the very late 1990s or very early 2000s.
After three years, I finally found it! It's a version of "The Emperor's New Clothes" with each new chapter written and read by the most random celebrities you could imagine. Check it out:

Technically this was a book on tape. I remember that this was a single story told from twenty or so different points of view (the story progressed linearly, but each new chapter was told from the point of view of a new character, some of which were inanimate objects). I also remember that each character was voiced by some celebrity, but the only one I can remember was Geena Davis as The Mirror (her first line was, "I am perfect.") Any help?