I just ran across a Slate slide show desribing a new way of laying out the periodic table [alt] of the elements. It turns out that Phillip Stewart's "Chemical Galaxy: A New Vision of the Periodic Table of the Elements" has actually been around since November 2004.
Check out the slide show:
(Here's an enlarged, legible image)
Basically, it's the old table, but wrapped so that the ends meet, and the tops converge in the center. The new arrangement's circularity manifests the table's periodicity quite elegantly.
The modern [standard] table artificially breaks up the sequence of elements at the end of each row. Certain elements fit into it uncomfortably; for example, hydrogen sits above lithium, with which it shares few properties. And entire groups are relegated to footnotes.... (slide 4)
Stewart has preserved the sequential march from light to heavy elements and all Mendeleev's groupings. But here the rows don't end abruptly, and related elements that were previously separated, like neon and sodium, have been reunited. There's no need for footnotes, and there's a convenient spot for neutronium (sometimes called "element zero" because it has no protons at all), which never found an appropriate perch in the old table. (slide 5)
The new circular arrangement also has the advantage of allowing the Lanthanides and Actinides (typically separated) to be visually integrated into continuity with the other elements.
Aside from possible diffculty to chemical novices, the only problem I can see is that the lettering is too small compared to the size of the table, making it difficult to see across the classroom for all but the largest poster sizes. Then again, maybe they just want to sell larger posters....
Also useful: Stewart's own Technical Notes
Susan Kruglinski, "A New Periodic Table of the Elements" Discover 26:6 (June 2005), 88. [subscription required]