Sitting out on a pedestrian mall on my morning coffee break, and the Lieutenant Governor of the province and his wife just walked by.
When I was a clueless teenager, my first trip abroad (alone) was to Barcelona. I hitchhiked from the airport into town, and got a ride from Matthew Parris, then a British Member of Parliament.
When I was a kid and teenager, and living in Wisconsin, one of our U.S. Senators, William Proxmire, could often be found out and about, shaking hands with constituents. I met him once outside of a Packer game, and on a different occasion, at the Kay-Bee Toy & Hobby store at the mall. 
Back in the eighties I was at a movie in Ottawa. Just as the lights went down for the show, I noticed Jean Chrétien and his wife slipping into the back row, quite unobtrusively.
In the late 90s I was on a plane home from Atlanta. While on the plane, still at the gate, people start applauding. I look up and see a soldier walking down the aisle and figured it was for him. I thought it a bit much but whatever.
Then I see president Carter walking down the aisle shaking hands with passengers. He came to my seat, said hi and shook my hand and moved on. Pretty nice guy it seemed.
I would have been terribly disappointed if he didn’t hand me a bag of peanuts with the Seal of the President.
That would have been truly great. His Secret Service agents should have always had a few boxes of peanuts on hand for such occasions.
I forgot…
When Obama was running for president he apparently had some offices or…something…in the federal buildings in Chicago. I happened to work less than a block away and I’d walk by them everyday on my way to the subway.
More than once I was at the corner when police would swoop in, block the intersection and a fleet of black Suburbans would come flying out of the underground garage and drive-by. I never actually saw Obama (tinted windows) but he had to be in one of them. This only ever happened then.
Bush II motorcade also whizzed by me going the other direction on the Kennedy Expressway from O’Hare airport in Chicago. Bumper-to-bumper traffic going to O’Hare and the WHOLE expressway going the other direction had no cars on it at all. The whole thing was cleared for Bush II.
It’s good to be king.
Passing through an airport I once saw Jesse Jackson and his entourage going the other way. No interaction as we were both busy,
Several…
Bill and Chelsea Clinton in line at a movie theater concession stand in Little Rock seeing Glory in 1989, while he was Governor of Arkansas.
Bill Clinton again at the urinal next to me in the bathroom of an FBO at the Philadelphia airport in 2014.
Prince Harry in 2007 at a bar in London, supposedly the night before he was going to be deployed to Afghanistan. He was there with several fellow soldiers getting lit.
There was a three-week period during March-April of 2019 when I went to see two different plays in two different cities, and somehow managed to have BOTH halves of a presidential ticket in the audience with me. One of them, Tim Kaine, I actually met. (I was with my dad, who knows him.) I am still kicking myself for missing my chance to see Hillary. It was obvious that somebody famous had walked in at the beginning, but I was sitting in an upper balcony and I didn’t know it was her until the guy next to me came back from intermission with a selfie. Damn.
I once shared dinner with then-ex-Senator Alan Cranston in Cancun. We just happened to randomly sit at the same table at a resort.
Many years ago I was doing some research in what was then the Public Records Office in London, when Norma Major, wife of the then Prime Minister, sat down opposite me at the same table. This was when she was working on her book about the history of Chequers. What made this amusing was how all the staff, who usually gave the impression of having been trained in customer service by GUM or Foyles, then went out of their way to help her in the most obsequious manner possible.
Even more randomly, I once saw the former Speaker of the House of Commons, Baroness Boothroyd, whom I had actually met formally on a number of occasions, in my local (long-gone) branch of Woolworths.
I was at a very casual waterfront family dining area a couple of years back when our Prime Minister, Jacinda Adern, wandered past with her baby on her shoulder.
Not particularly famous, but back in the 1990s, when I was living in Indianapolis, I was having lunch in a McDonalds when Steve Goldsmith, who was then mayor of Indianpolis, came in and ordered a cheeseburger.
A long time ago, ex-President Nixon lived in San Clemente. Ex-President Nixon liked to golf and was a “member” of a club close to the beach. As I recall, he golfed in the morning, once a week on a weekday. Nobody else golfed at that time, nobody was allowed in or out of the entire course and club.
Once the doors of the 19th hole were closed and locked, all food and drinks drinks were on the taxpayer dime until that single man finished up. I have no idea how good a golfer he was, but he sure looked sad and lonely.
This was almost 40 years ago, but I just read Matthew Parris’ Wikipedia article and discovered something I never knew before:
At the age of 19, Parris drove across Africa to Europe in a Morris Oxford; the trip was traumatically punctuated when he and his female companion were attacked, and he was forced to witness her rape.
He picked me up late evening in darkness at a dubious spot for hitching, and was incredibly nice, insisted on driving me all the way to the door of a cheap but good place to stay in the city. He obviously had no way to know I was also from the U.K. until I got in the car. Probably his kindness to a random kid hitchhiking incompetently was influenced by his horrific experience.
I was in one of the airline executive lounges in Dulles waiting for my flight to Denver, when the then mayor of Denver, Wellington Webb, came in with his entourage. As I expected, we were on the same flight, but he was up in first class. Didn’t talk to him or anybody in his group.
I’ve occasionally seen my MP shopping at the supermarket. And, though not a politician, I did once nearly tread on Prince Charles’s toes during the end-of-lecture rush when we were both students at Cambridge.
In 1978, our family spent a long weekend at Le Chateau Montebello, in Quebec. One evening, my parents were enjoying a pre-dinner cocktail (Sis and I had soft drinks) in the lobby bar. Through the lobby walks Claude Ryan, who was then the leader of the Quebec Liberal Party. He and his associates looked to be heading towards the dining room; and sure enough, when we were seated in there, they were only a few tables over.
Not me, but my ex-wife. Early 2000s, and my ex is on business in Ottawa. She was walking past the Tomb of the Unknown Soldier, and a couple of limos pulled up to the curb. Out of one, appeared Jean Chretien, then Prime Minister. My ex, recognizing him from TV news, waved and said, “Mr. Prime Minister! Good morning!” He waved back, said “Good morning,” and actually extended a hand. My ex shook it, they exchanged pleasantries (“It’s nice to meet you,” sort of thing), then she went on her way, and he went his.