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Cleaner code, the seperation of content from style.
And more importantly than that, the positioning of content within the page source.
It also creates smaller size pages, generally. And almost always a higher ratio of "content text vs. markup text".
Don't forget the user perspective either (thinking like a user is the first step in truly understanding SEO) - getting tables to render on mobile devices is tricky, and that's becoming more and more important. It's not inconceivable that at some point in the future SE's will serve different SERPS to users on mobile devices based on accessibility.
fixed sites built with divs or liquid built with nested tables and clear/spacer gif's better?
why the separation between fixed width and liquid design? you can get a liquid design in CSS.
But fixed vs liquid doesn't have any effect on serach engine listing - but can have some on usability and accessibility [webmasterworld.com].