Douglas Hofstadter has an interesting discussion in a Presidential lecture at Stanford. Skip the introductions and start at 13 minutes 30 seconds to listen to Hofstadter.
Hofstadter believes that analogy making is at the core of all cognition, and what is especially interesting is how frequently analogies seem to occur in everyday experiences and how complex the parallels can be when suddenly we have a flash of insight, "That's just like...(something else)".
It's probably true that we don't think about using analogies as much as we should in education. Analogy-making abilities exist in preschoolers and studies even suggest that the use of analogies in present new concepts to young elementary school children improves learning and retrieval.
Another interesting read is Gentner's Analogy. In it, Dr. Gentner recalls an interesting study by Gick and Holyoak that found 30% of people primed with an analogous story thought to use it in solving a unique problem (10% solved it without the priming analogy); however, test subjects were simply given a hint to think about stories they had heard, 80% were able to solve the new problem (the problem was how to kill a tumor without too much surrounding irradiation; the analogy involved soldiers converging on a fort). So part of the dilemma for getting students (and adults for that matter) to solve problems - may be that they aren't accessing analogous situations from their fund of knowledge or memory. Perhaps some of the inventive souls and creative thinkers (like Hofstadter) are more attuned to analogies in their thinking and this gives them their creative edge.