When this thread started, I thought the topic was more like "who's the most famous person on your cellphone" type of thing. But since it's not, I'll add some conversations I've had over the years that I recall being interesting at the time.
I was a seatmate on a shuttle flight with Bob Novak (who, if alive today, would be a superspreader as he coughed the entire flight w/o covering his mouth). We had a long conversation about Scott Peterson and why American news doesn't cover significant world stories but focuses on ratings grabbing garbage.
Also an aisle mate with Nomar, on a flight from Dallas where he reinjured his wrist in 2001. He was the first person I'd actually ever saw with a personal portable DVD player. It was just him and me in the aisle and I didn't bug him much, but I did a double take on boarding, with a look like, "Wait, aren't you supposed to be playing baseball somewhere?" So he told me what was going on, it wasn't public info, and at that time there was no in-flight internet or Twitter, but I have to say I was tempted to use the airphone to call WEEI.
Living in Alexandria, I'd bump into all sorts of people and have brief conversations, James Carville while grocery shopping a couple times (I once asked him who cooks in his house and barely understood a word, but the essence was if it was something with flavor, he cooked it), George Will at a bookstore (we discussed the Mussina to Yankees trade), Louis Rukesyer over G&Ts in the USAir Club (tech stock valuations). I found them all approachable if you didn't come at them like a fanboy.
And when I was involved with the old Internet World conferences, I met dozens of people who went onto become CEOs of major tech companies before they had entourages. Fun times. Wish I'd invested more.
Also, our coffeehouse received a few visits from pols during the 2008 elections, resulting in photo ops with Ed Rendell and hanging out with Dick Durbin for a half hour talking baseball. Rocky Blier, Cyril Wecht, Rep. Tim Murphy, Dave Wannstedt were regulars, Michael Keaton popped in occasionally.