I don't have a big fascination either, but I do get a kick out of some of these stories hearing funny or interesting interactions, many showing who these people really are ie Chevy Chase or that they are regular people.
Met Jackie Mason in a NYC restaurant as he walked by our table and said "oye, crowded in here tonight", and we all cracked up just hearing his voice. For you younger people, pull it up on Youtube and you'll understand.
Checked the IDs of the whole band Anthrax when they came into the bar I worked at. I had no idea who they were, even the dude with the long beard.
Took a leak next to a VERY drunk Bruce at a restaurant/bar down the shore 25 years ago.
Met Dwight Gooden while getting a haircut in Metuchen. Very nice guy, talked to me an my son for 10 minutes.
Saw Charles Oakley in Miami airport.... gave him a very wide berth as he did not look happy, so I never said hello.
Met the former and current POTUSA, plus once when he was "just" the guy on the Apprentice. Talked golf briefly. Also met his daughter... failed to make a lasting impression....
Met Supermodel Nikki Taylor. Also failed to make a lasting impression.
Met Elle MacPherson at a Knicks game. Once again, failed to make a lasting impression... but whatever perfume she was wearing was amazing.