My favorites are some of the times I've seen bands and wondered, "What are you doing here?"
A long time ago, I was attending a company event at DisneyWorld during one of those special nights when the park is "only open to High School Students" (plus a certain number of creepy corporate types). I was one of the creepy corporate types. Anyway, I was making my way to some ride, turned a corner, and there was Wang Chung. They were playing Dance Hall Days. I had to stop and watch to see if everybody was going to Wang Chung tonight. (The band did, but they were the only ones.)
In the early 80's, Chicago used to host Chicagofest down on Navy Pier. It was fantastic. For about $10, you could buy a wristband to spend the entire day seeing as many bands as you could squeeze into your day. I was rather poor, but I scraped the cash together and saw Cheap Trick, Point Blank (no, no one else remembers them, either), Shooting Star, the Doobie Brothers (I was underwhelmed), and several more that I really can't remember. It was funny to walk around through the crowd and see these guys walking around with the normal folk, trying not to be noticed.
Going back a little further, I was wandering around at the 1974 World's Fair in Spokane, WA and saw Grand Funk Railroad performing on an outdoor stage. The band piled together in one small circle on the stage, almost on top of one another, leaving the rest of the stage completely bare. In retrospect, I think it was a way to compensate for inadequate monitors. Bachman-Turner Overdrive was a bigger hit and the small crowd seemed to know who they were. It was a little strange to walk through the park and accidentally come across one of these bands. The surprise made it that much more fun.