Oh, wow! I did not expect to see so many replies to my question! And I also didn't expect such a wide variety of replies too!
Here is what I was guessing the differences would be. It's a completely data-less guess though.
The "K" lenses, which are not specifically marked as "K", came out to coincide with the K series of bodies (K2, K1000, etc). All of the optics were based on the previous M42 lenses. There were probably some tweaks here and there to the design and a few extra focal lengths were added.
The "M" lenses came later with the release of the "M" series of bodies (ME Super, MX, etc). Based on what I read around the web and what others have said here it seems like the "M" series of products were designed to be slimmer, smaller, and targeted toward the larger amateur audience. These were the people who simply wanted to take pictures. They weren't so concerned with resolution as the enthusiast or professional of the day. These lenses weren't bad at all but compromises were made to make them smaller. The pictures produced were still "good".
The "A" lenses are an extension of the "M" lenses. They still retain the compact design of the past but the elements were redesigned so that the optical performance matches the "K" series of the past. Pentax must have learned a thing or two since 1975. Coatings were tweaked a bit too. These lens designs were the pinnacle of perfection and would not improve until the digital era came upon us.
So, in terms of desirability, the order would be A - K - M.