The coolest moment have all had to do with astronomy.
(1) Back when I was about 17 or so my older sister and I went to the local Christian Serviceman's center. When we got there, I happened to notice that the full moon was ever so slightly eclipsed, and there was a group of people standing in the driveway looking at it. Someone asked, "Exactly what are we seeing here?" and my sister gave me a nudge, so I started explaining the mechanics behind lunar eclipses to a rapt audience, most of whom were older than me.
(2) Fast forward to May 1994, the day of the big annular solar eclipse that was seen in a wide swath across the United States. Since I'd known it was coming, I wrote an article and submitted it to the newspaper of the military base where I was working, and it was printed.
The day of the eclipse, I had my eclipse-watching kit (14 layers of Mylar taped together and a box with a pinhole in it) and I was stationed at a window of the hospital where I worked that had a perfect view of the eclipse. I was on the third floor, and happened to look down and notice a group of people with their pinhole boxes down on ground level. In my article I had made a point about not looking directly at the sun and instead using a pinhole box to watch the eclipse. As the eclipse progressed I was joined by a group of people at my window, so I passed around my Mylar. Someone asked what we were seeing, and someone else mentioned the article in the base paper, to which I said, "I wrote it," so I got to give another impromptu lecture on the orbital mechanics of the sun and the moon to another rapt audience, this one made up mostly of military officers.