I think the best information that comes from someone's About Me isn't the actual content that they put there, but the meta-content. The truly informative aspect is their choice of what sort of content to put, and their choice of how much information to put. It's not about the information they actually provided, but the information that they gave away by their choice of what information to provide.
Type of information chosen:
Whatever information is there, they feel is important, or even essential, in the sense that it is meant to portray their essence. Alternately, or more likely simultaneously, it is information intended to create an impression, an image: the type of image that a person tries to convey says a lot about who that person is beneath the projected image. Ultimately, every piece of information delivered is trying to create an image. What varies is the closeness with which that image corresponds to the reality of character/personality, which depends upon the writer's openness and degree of self-knowledge.
Yet another component is the writer's perception of what readers will consider important information about him/her, or perhaps about what readers will consider interesting. Obviously this aspect is related both to the image being created and to the writer's self-concept, as well as to the writer's expected audience, the writer's attitude toward that audience, and the writer's attunement with said audience.
Amount of information:
Some people put their whole lives into their About Me. Others put cryptic statements like "Ask me." This can depend on a number of different factors: how much someone actually wants you to know about them, how much that person thinks you would be interested in knowing about them, how paranoid that person is about unexpected readers...
The really cryptic About Me's are ones that don't actually contain any of the person's own words, but rather lyrics or a poem or a quote. I usually have some idea of how to interpret About Me's in people's own words, but when they quote someone else, I have no idea what to think. Do they just really like that song? Do they feel it describes them? How specifically / literally might it describe them? etc. Perhaps most cryptically, what reaction do they expect me to have to that song?
I suppose you can tell by this post that I think you can get a lot of good information about a person indirectly. My analysis here, in particular, is awfully revelatory of my character...
That said, I would also like to mention that I am the sort of person who, almost without fail, takes the stairs two at a time. When I'm going down stairs, I also have a strong tendency to skip & leap. People look at me rather oddly for it, but the physical pleasure of flying briefly is definitely worth it.