To understand the Obama Ayers relationship, one only needs to look at basic network theory. In actuality, the fact that Obama and Ayers have a relationship is no information at all. It would have been virtually impossible for two policially active people in Chicago to NOT have some relationship.
In 1973, Mark Granovetter published his famous paper "The Strength of Weak Ties," which went on to become one of the most cited papers in history. The basic insight of the paper was that through friends of friends and their friends we know an enormous amount of people. Through our "weak ties" we build a vast web of relationships that quickly grows into millions of people.
This effect has been documented extensively and in many different contexts. If you are on a corporate board, you are just a few links away from every other corporate board member in America. If you have acted in a movie, you have probably played with someone who played with Kevin Bacon (or anyone else who has played in a movie). If you have co-published a paper on mathematics, you are every likely to have written it with somebody who has ties to Paul Erdos, etc.
The real issue isn't that Obama knew Ayers, because it would be virtually impossible for two people active in Chicago politics and interested in educational issues not to have had some contact. We're only talking about a few thousand people and the business of politicians is to make contacts with people who in turn have contacts with others. The fact that they knew each other has absolutely no informational value at all.
Did they ever meet alone or socially? Did Obama ever act on his behalf? Were there financial ties?
As far as I know, the answer would be no to all of these questions. Unless, of course, we were talking about the McCain/Keating relationship...