This version was Adobe's first identity, designed by Marva Warnock–wife of the great font designer, John Warnock. Creativity runs in the family, apparently.
My first thought was that the trapezoidal footprint rather reminded me of a mesa, which reminded me of the American Southwest, which reminded me of adobe houses and such.
The old logo is quite delightful, I find; note the way the right-hand slant on the A is carried through the rest of the design rather aptly. The stylization is also extended through all glyphs in a rather aware and accomplished way. Mrs Warnock certainly knew what she was doing with this one (we think perhaps a font based on this would be called "Mrs Warnock", like the font "Mrs Eaves" honors the eventual spouse of type legend John Baskerville (though it must be said that the Warnocks undoubtedly had a much less complicated courtship than the Baskervilles did).
The original logo also gives us a glimpse of what the future logo would look like–the stylized A has come forward with very little change–just an adjustment to the aspect ratio and the grounding to the baseline of the right-hand slant stem stroke, thus here's another example of how a company respects and extends its own graphic history.
(Credit where due: A Google Alert led me to a post at FrogBlog, which pointed me to the recently-debuted "World's Best Logos" blog, which is a little light on content, but has some gems which are worth looking for graphically–little original content, though, as the text is largely cut-and-pasted from other sources. Still, at least someone is trying to document it all)
Tags: logo design, logos, historic logos, Adobe Systems, Adobe