I don't remember a time when I wasn't in some sense interested in rationality in some sense... but I can remember one time being at a bookstore and seeing Bertrand Russell's "Why I Am Not a Christian" (this being back when I was one) and thinking "Maybe I should read that and see what the other side says." I came home with it and my mom saw it and asked why I would want to read that when it might make me doubt. I clearly remember thinking about it and responding with something along the lines of "If you don't know both sides, how could you possibly know which one is right? Wouldn't you rather be right than keep the same wrong beliefs?" I don't know that it was a turning point for me, but it was the first time I had really had that thought out loud (and it was probably the start of my deconversion and subsequent start down the road of rationality).
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).