(this is basically the same question, only in math, as Alessandro Cossentino asked about theoretical computer science at TCS.SE: https://cstheory.stackexchange.com/questions/8869/casual-tours-around-proofs; if a question similar to this one already exists at MO, feel free to close this)
Recently Ryan Williams published (see http://arxiv.org/abs/1111.1261) a more "pedagogical" version of his proof in complexity theory concerning NEXP and ACC - in his own words, "the proof will be described from the perspective of someone trying to discover it". The paper discusses more intuition, failed attempts at solving the problem etc. much more extensively than a typical journal paper.
Personally I find such efforts extremely valuable, because they give you an opportunity to learn how somebody thinks about mathematics and not only verify the formal correctness of some abstract reasoning.
What other examples of such approach are you aware of?