When I was a teen, I was a busboy at a restaurant where Donna Dixon sister was having a wedding rehearsal dinner (the Dixons were from my home town). Donna Dixson and Dan Akroyd were at the dinner and Dan Akroyd came back to the kitchen to thank everyone and take pictures, etc. this was peak Ghost Busters fame and he couldn’t have been a nicer person. He made a point of meeting busboys, dish washers and cooks.
Congressman/politician John Garamendi: My mom worked for him for a number of years and he’s been a family friend since I was about 10. He even officiated our wedding.
Bill Clinton: I followed him around with a video recorder at a megabuck campaign dinner, so I actually got to talk to him more than anybody else at the dinner. I was amazed at how he managed to connect with each person in the room in their one-on-one conversations. For instance, one of the attendees was from Mariposa County (CA), and Clinton talked about a roommate he had while at Oxford who regaled him with legends of Joaquin Murrieta, the alleged gold rush era outlaw.
Former California Governor Edmund G. Brown Jr.: had a very brief conversation with him at a Garamendi campaign event.
Pete Seeger: Ibid. Seeger is a supporter of Garamendi and used to attend fundraisers.
Former Raider and NFL Player’s Association head Gene Upshaw: He and Garamendi were buds from their football days, and Highway 63 would come to campaign events. Since my mom knew I was a Raiders fan at the time, she tasked me with meeting him at the door and leading him to the VIP area. From a distance, he looked like any ordinary guy, but as he got closer, he just got bigger and bigger and bigger. When we shook hands, it felt like I was shaking a country ham.
Olympic and World Judo Champion Yasuhiro Yamashita: not much of a conversation, because my Japanese and his English (at least at the time) were both equally bad. Met him shortly after the 1984 Games in LA, when he was on a world goodwill tour with…
Japanese Olympic Judo Coach and former World Judo Champion Nobuyuki Sato: ibid.
It wasn’t a conversation, but political activist/politician Tom Hayden once scowled at me when I suggested that legislators were just regular people who happened to be elected to work for their constituents.
I forgot that I waved at Bill Clinton (and he waved back) as his limo passed in front of us at the back gate of LAX.
Have I ever mentioned I had a beer with Willie Nelson? 
The best I can come up with is Simon Townshend (Pete’s brother). I had a brief chat with him after a solo gig at Cafe du Nord in San Francisco.
In a book lover’s chat room on AOL we all knew a guy who had written a couple of novels and was working on a non-fiction book. I exchanged some private messages with him. The book he was writing was Kitchen Confidential. He was Anthony Bourdain.
Beer?
Ralph Nader, Cleveland, 2000.
Donna Douglas (Elly May on the Beverly Hillbillies)
Patty Duke
Carl Reiner
Jerry Mathers
Sonny and Cher
Kid Rock was at a relative’s wedding and he was quite humble.
Aside from that I have briefly met numerous people running for President but those conversations were nevermore than 30 seconds long.
Since the last time —
David Gerrold – twice. I had dinner with him, and months later I was on a panel with him.
Jeff Wayne.
I hear he tends to be pretty down to earth. First thing out of his mouth is “Call me Bob.” Too bad about the politics.
Isaac Asimov - on the last MITSFS picnic he went to when he was still living in Boston. Also at cons.
Hal Clement (Harry Stubbs) - ditto
Alicia Nash. I worked with her on the MIT Alumni Club in Princeton, and was at her house and she was at mine. John Nash was still sick back then, he wandered out during our meeting at her house and she shooed him back.
Adam West - on a set. My wife met Iggy Pop during another show - I’m jealous.
Arno Penzias - he funded a research project I was leading, and I got to give some talks to him.
Amar Bose of Bose research, at a party one of my MIT professors had
Marvin Minsky - I had an interview with him when I was thinking about going into AI, back in the early 70s. Luckily I didn’t - I would have graduated right into the AI winter.
Don Wollheim - we gave him and Elsie a tour of the MITSFS library during the first Noreascon.
Keith Laumer - ditto.
Terry Pratchett - during a book signing.
JRC Licklider who got funding for the start of the Internet, at a mini-seminar at MIT. Also other AI stalwarts who probably aren’t famous enough to count.
Salvador Luria, Nobel Prize winner in Medicine in 1969, who taught the Bio 101 class I took. I count him because he came and taught a quiz section when the TA was at a conference.
Biggest disappointment for someone I never met - Claude Shannon’s office was across the hall from my lab, but he never showed up there.
Actually had a conversation with? A few that are famous to me, but probably not to y’all, unless you’re into progressive rock…
I had an email correspondence with Jordan Rudess, keyboardist of Dream Theater, several years before he joined DT. Nobody knew who he was back then, outside of prog rock circles. He popped into rec.music.progressive looking for opinions on his latest solo album, and I was happy to oblige.
There’s a prog band out of Mexico that’s been around for about 40 years, called Cast. In the mid-90s I left some feedback on their website, and the founder/leader tracked me down and called me out of the blue in order to sell me all of their albums to that point. It worked.
In 1994, a UK band called IQ flew out to San Jose to play a single show. I met all of the band members, and chatted with most of them. Also chatted with members of Enchant, a local prog band, who opened the show. Their singer eventually went on to join Spock’s Beard.
I met Persi Diaconis once. I went up to him after a talk he gave and spoke to him because he had cited (and summarised) a paper of mine in his paper (joint with Dave Bayer) Trailing the dovetail shuffle to its lair.
Almost anyone famous I have met is a mathematician. Notably Paul Erdös, whom I met many times. At least as famous among mathematicians is Alexander Grothendieck, the leading mathematician of the 20th century–at least the second half. I once met future Canadian PM Kim Campbell when she was 23 and at a math meeting trailing future husband Nathan Divinsky. I did once meet singling cowboy Gene Autry, but I was only about 8 or so and too shy to say anything, Finally, Orchestra conductor (Oregon Symphony mainly) James Anderson DePriest was a HS classmate (Marion Anderson was his aunt).
I worked in San Diego theater for a bit.
Robert Hays gave me some good tips on back stretching.
Penn and Teller were really cool. We (the tech crew) frequently played basketball and had some beers after work, and they’d hang out and shoot the shit.
Neil Patrick Harris came to our opening beach party and played volleyball.
David Morse was pretty reserved, kinda kept to himself.
Barry Manilow was nice enough. He was the writer of the show, so he was very busy.
CCH Pounder was lovely.
John Goodman was a hoot.
Tovah Feldshuh was horrible to some of my fellow tech people, specifically costumers.
George Mitchell spoke at my high school graduation, and I spoke with him afterwards.
Similarly, Mandy Patankin was the speaker at my grad school graduation.
At the age of 9, I met and briefly spoke to Canadian Prime Minister Brian Mulroney and his wife Mila following a concert at Quebec’s Notre Dame Basilica.
In 2000, I met Toronto singer and actress Melleny Melody (Melleefresh) on Bloor Street near Bay as she was decorating her moose (in the same basic kitschy style as her art car) for the “Moose in the City” event.
Two or three years later, I met actress Jackie Burrows on around the same place. I came up to her and greeted her and we had a brief conversation.
Morgan Freeman I used to play at his Ground Zero Blues Club in Clarksdale, MS.
Mel Blanc He spoke at WVU. I got his autograph.
George Will I saw him sitting in a concourse in Logan airport. He was writing or doing paperwork, so I greeted him, said I enjoyed his writings, and that I could see he was busy, so I wouldn’t keep him. He seemed genuinely pleased, at both the compliment and the briefness of the interruption.
Honorable mention Steve Jobs I didn’t have a conversation with him, but sat across from him in a meeting. This was in the early 1990s, after he got pushed out of Apple and started NeXT computers. Our Agency bought a few of them, and he came to give a demonstration (it didn’t work) and talk with programmers later.
George W. Bush I shook hands with him in a receiving line when he came to the Agency where I worked in 2002. I said, “It’s an honor sir”, he replied, “It’s an honor for me too”.
Not-so-honorable mention G. Gordon Liddy In my misguided youth, I read and enjoyed his book. When he came to speak at WVU, a police officer friend got me backstage to meet him to get his autograph in the book. (We all do stupid things when we’re young.) FWIW he was very gracious.
I’ve seen (and heard) Mel Blanc speak twice, at two different Universities, but I didn’t talk with him on either occasion.