This is an old and self-indulgent story; but it was such a charmingly unexpected bonus from my early use of MathOverflow, that I think it deserves to be recorded somewhere (my apologies for its length!):
tl;dr: As a serendipitous consequence of this MathOverflow question, the second answerer invited me to give my first-ever seminar talk as a grad student.
At the time I was a 2nd year grad student in topology, working on a project related to knot signatures. Specifically, I was hoping to relate this paper by Kirk and Livingston to some possibly novel computations I'd made, but I was having some basic difficulties, leading to this MathOverflow question. My question didn't mention the paper, since my confusion was quite preliminary to its content. In addition to a great answer by Emerton, I got another great answer from a mysterious user "Paul." In an illuminating response to my follow-up comment, Paul even mentioned the paper I'd been reading! In my surprised reply, I explained that this paper was in fact directly responsible for my question.
Paul eventually revealed by email that in a miraculous coincidence, he was in fact P. Kirk, one of the authors of that original, motivating paper! (This possibility had certainly never occurred to me). After more email exchanges, and more due to his kindness than my results, Paul actually invited me to talk in the Bloomington topology seminar, to discuss things in person. This led to my first ever "invited" seminar talk (Wayback Machine), and a truly fantastic visit to Bloomington, very formative as well as informative!
My computations themselves were never actually published, but they did make it into my thesis, which is on the arXiv (Chapter 3). This story, however, is not in my thesis! I'm glad I could record it somewhere. Please edit if appropriate!