Some previous threads:
Famous people you’ve seen in person (2009)
Brushes with Fame-Celebrity Encounters (2012)
Which famous people have you met? (2016)
A couple I’ve met:
Barry Goldwater.
This was around 1988 or so. He paid a visit to a lab I was working in. He was in a wheelchair, and some guy was pushing him. The only people in the lab were me, my boss, Barry, and the dude that was pushing him.
Political commentator Mike Gallagher.
Met him numerous times when I was 13 or 14. Strange story.
Michael Jordan, maybe? Many times? He even stepped on me during a game.
I worked at the skywalker ranch so…just one story.
Once I went down to make some coffee and when I got back to my desk I mentioned to a coworker that someone was dressed as the Dalai Lama and he responded “That is the Dalai Lama downstairs”
As no one was ever in costumes there, as they were just working I still can’t figure out why I assume that he was.
Up close and addressed directly? Bill and Hillary Clinton; Mitt Romney, Pudge Rodriguez; a score of Members of Congress; Penn Jillette and, in an entirely separate and independent circumstance almost 20 years earlier, Teller; Jim Lovell; Eugene Robinson; Ed Rendell and a squad of other former Govs.
The best I can do is Rudy Giuliani and Chuck Schumer. They both spoke at a college graduation that I attended. I didn’t realize they were on the bill until after I arrived.
I’m not averse to seeing or meeting famous people, but I do usually avoid the sort of crowded and/or glitzy venues where they are most likely to be spotted. I lived in New Hampshire for two presidential election cycles. If I’d wanted to, I could have met and shook hands with just about everybody running for president in the run-up to the primaries. Several of my relatives do that. But it’s not my sort of thing.
I was within about 8 feet of Bertrand Russell at a nuclear disarmament rally in London in 1961, but didn’t actually meet him.
Billie Joe Armstrong, of Green Day, when he was seven years old.
SF writer David Brin came to talk to my creative writing class because he was friends with the teacher. I also went to a Christmas party at the teacher’s house, and SF writer Harry Turtledove was one of the guests.
Met Barack Obama, first when he was running for Senate in '04, then again met him in '08 during his prez run. Both times were union rallies in Chicago that I was working on.
In my job I’m around famous people frequently.
Recently worked with a certain 7-foot tall athlete. I’d never met anyone that big before, and it’s pretty startling at first. Very nice man, and I was struck by the realization that he must have a pretty challenging life. Other celebrities can, to some extent, hide under a ball cap and baggy clothes if they want to. But there is no hiding when you are that big, and an instantly recognizable face to boot. It has to be tiresome.
I’ve responded to similar threads in the past with people like Stephen King, Leeza Gibbons, some musicians and athletes; but this reminded me that I once held the elevator door open for Steven Weinberg.
I’ve never seen any celebrity that was not either at their own event nor trying to be seen. The ones that were trying to be seen were people I didn’t know and I only knew they were a celebrity because other people recognized them. I did play a board game with Dave Arneson, co-creator of d+d, without realizing it, but the fact that I had to mention that he was the co-creator of d+d along with Gary Gygax sort of removes the name recognition to it.
Then again, I’ve been at lots of concerts at The Social in Orlando where you can usually get within 10 and often 5 feet of the band. So just by bands that would be recognized mainstream, by that criteria I’ve seen The Church, Dashboard Confessional, New Found Glory, and Fountains of Wayne up close.
Patrick Stewart
Ray Bradbury
Was within 10 feet of Pele once while he was signing autographs (didn’t have pen or paper with me, alas).
I met and got cards signed from several of the better-known players from the ‘72 Summit Series - including Tretiak. 
Also, how could I forget? I saw Kate Bush at a fan event in London back around 1990 or so.
The Queen when she was doing a walkabout outside the Saskatchewan Legislature. Not close enough to say hi.
I volunteered on the county Fair commission and was able to meet several up and coming country singers. Joe Diffee, Hayes Carll, Alabama Shakes, several more aren’t coming to me right now. I am not much of a country fan. I know it cause that’s about all they play around here.
Toss-up between Francois Mitterrand (at the Paris Heliport) and Margaret Thatcher (spotted in a limo during a G7 summit held in Paris).
I guess Lorde would be the most famous non-classical musician I’ve seen in concert.
I guess I’m not very familiar with a lot of celebrities. I did used to work with Yannick Nézet-Séguin, who now conducts the Metropolitan Opera in New York, but I don’t know how many people in general would know who he is.
That the Broadway version? I saw them, too, though from the balcony.
I was in the 4th row to see Tony Shalhoub, Anthony La Paglia, Brooke Adams, and Justin Bartha in Lend Me a Tenor.
The science fiction writers I know or have seen are a long list. The better known ones include Samuel R. Delany,* Gene Wolfe, George R. R. Martin,* Terry Pratchett,* Neil Gaiman,* Harlan Ellison,* Isaac Asimov, Anne McCaffrey, David Drake,* Steven Erickson,* Moebius, Gardner Dozois*, Larry Niven, David Weber*, Ramsey Campbell*, Hal Clement,* Michael O’Hare (Babylon 5), Hal Clement*, Octavia Butler, Tim Powers, Joe Haldeman,* and many others (asterisks are those I’ve actually talked with).
Non-SF include live stage performances by John Astin, Charlotte Rae, Bette Midler (Fiddler on the Roof), Valerie Harper, Gilda Radner, Sam Waterston, Mary Frann, Peter Bonerz, Melinda Dillon, Linda Lavin, Jo Ann Worley, Petula Clark, Georgia Engel, Richard Thomas, Pamela Reed, Christopher Lloyd, William Daniels, and Jack Cassidy.