As many of you know, I never read fanfic, however I was told this story was exceptional and found it a totally worthwhile (though not of course flawless) foray:
http://www.fanfiction.net/s/5782108/1/Harry_Potter_and_the_Methods_of_Rationality I've got as far as the author has - the story isn't yet complete but its gone a long way and, though it would be sad if it isn't finished, this rationalist re-envisioning of HP remains an excellent, complex read. I enjoyed it far more than the original, partly because I found its flaws far less painfully gaping and because it highlights and addresses some of those things which made me wince in Rowling's version.
The fanfic.net reviews contain spoilers and an interesing range of praise and criticisms. Some of the reviewers seem to have reread the entirety up to 7 times and are still enjoying it. I think I'm about to start re-reading the story myself.