I can't really relate to the religious stories, my parents, though not atheists, are pretty secular so I never had the brush with religious indoctrination. In reality I've probably always been an atheist. I think this gave me an early start on rationality, not so much because atheism taught me rationality, but because I never had to abandon a rational line of thought for fear of challenging my religion.
As for consciously trying to be rational though I don't know of any one defining moment though I can recall a slight watershed. During grade 11 I was selected to go with some other students to an economics conference. The conference was run by a strongly right wing institute and myself being left wing, and wanting to signal my intellect by challenging much older and much more knowledgeable people got into (and probably made a fool of myself in) numerous debates.
I recall over the next several months starting to realize that my own views and conclusions might be mistaken. For the first time I started seriously considering how to actually think about and try to find the truth which is probably the same place I'm at today.
To break up the awkward silence at the start of a recent Overcoming Bias meetup, I asked everyone present to tell their rationalist origin story - a key event or fact that played a role in their first beginning to aspire to rationality. This worked surprisingly well (and I would recommend it for future meetups).
I think I've already told enough of my own origin story on Overcoming Bias: how I was digging in my parents' yard as a kid and found a tarnished silver amulet inscribed with Bayes's Theorem, and how I wore it to bed that night and dreamed of a woman in white, holding an ancient leather-bound book called Judgment Under Uncertainty: Heuristics and Biases (eds. D. Kahneman, P. Slovic, and A. Tversky, 1982)... but there's no need to go into that again.
So, seriously... how did you originally go down that road?
Added: For some odd reason, many of the commenters here seem to have had a single experience in common - namely, at some point, encountering Overcoming Bias... But I'm especially interested in what it takes to get the transition started - crossing the first divide. This would be very valuable knowledge if it can be generalized. If that did happen at OB, please try to specify what was the crucial "Aha!" insight (down to the specific post if possible).