I've never bumped into any movie stars or anything, but I've gotten some good sports autograph stories.
When I was a kid in the early 80s, my stepfather and I saw Rickey Henderson coming out of a sandwich shop in Berkeley. We stopped the car and jumped out to get his autograph. He was very cool, nice guy. This was long before he set the stolen base record, so I'd imagine that autograph might be worth something now.
We went to a Reggie Jackson signing about 10 years ago, and had him sign an A's program from when he was on the team. I guess he'd been signing baseballs and other boring items all day, because he stopped to check out his own picture in the program before he signed it. My mom and I got a laugh out of that. He is EXACTLY the way you'd expect him to be.
The all-time greatest autograph feat was when my stepfather was driving through Martinez one day about seven or eight years ago and saw an old man walking down the street. He pulled over to get a look, and confirmed that it was Joe DiMaggio, who also happens to be from Martinez originally. Now, DiMaggio is my stepfather's IDOL. He knew he'd never get an opportunity like this again, so he walked up to Joe and asked for his autograph for his son (my brother, who was a star of his Little League team at the time). Joe signed a scrap of paper that said "To Adam, Best Wishes, Joe DiMaggio". Later, we read that A) He never signed anything for free, and B) He specifically never wrote any personal sentiment like "best wishes". So this was a real one-in-a-million encounter. The autograph is framed now, with a beautiful photo of DiMaggio in his playing days in the 40s.