For me it’s 3:
My mother used to work for Kurt Vonnegut Jr.'s son.
Neil Diamond is the first cousin of my best friend from high school. Or maybe his mother’s first cousin.
I still never met him.
I never meet anyone famous, but I guess I have loads of somewhat close connections to famous people. My favorite is that my uncle’s mentor when he was studying psychoanalysis (and whom I’ve actually met myself, very briefly) met the guy who assassinated Trotsky, just before he left for Mexico to do it. So I guess I’m one degree away from Trotsky’s assassin.
My dad was one of the pilots who brought the Vietnam POWs back the U.S. after their release. That’s two degrees, though I don’t know specifically who was on his plane.
One of the Iranian hostages lived on my paper route.
A reasonably well-known actor has been a trainee on the same ship I was on, so I know some people who know him pretty well.
My uncle is a “famous” former rugby player and coach.
My father has worked for NASA off and on for a large part of his life-- John Glenn gave him his nickname. That pretty much puts me 2 to 4 degrees from ANYONE 
Let’s say I’ve had some encounters with a few celebs - This is long -
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Well, let’s see… ummm… my ex husband (we were best friends at this time) was at one of his friend’s house one afternoon. This was back around 1983 or 1984. The phone rang and he answered it. It was Tom Selleck calling for the sister of his friend to ask her out on a date. This was also when the Magnum PI series was on TV. He said it was surreal because that’s just not who you expect to hear on the phone when you answer it.
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One of my friends dated Macgyver, aka Richard Dean Anderson for about a year. She said that even when they were out on a date, if he thought they were going to encounter a bunch of admiring women fans, he wanted her to pretend that they weren’t together so that they could all still fawn over him and think he was still single. She said that got really old and sickening. He was very vain. She left him. Period.
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I saw lots of celebrities when I was a flight attendant for American Airlines. One of the most sickening was Michael Bolton.He had this chick with him up in first class. From the moment they got on the plane, they started sucking face like no one else was around. When I and another one of the FA’s asked him to stop, he started screaming “Don’t you know who I am?”
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The next most sickening was the baseball player Reggie Jackson. He was on one of my flights from JFK to LAX. The other flight attendants warned me about him as did another male passenger. Shortly after the flight took off he got up and started wondering around in first class. We were on a DC10. At one point I was in the galley by myself. Ole Reggie walked in and pulled the curtain closed. I was getting several drink orders ready on a tray. He didn’t say a word and many minutes passed. He leaned up against the counter, pulled out this huge roll of money and started thumbing through it. I never looked directly at him, just continued to prepare the drinks. It was so weird! What did he think I was gonna do when I saw his money? :eek:
Finally he started asking me a few questions. Luckily I was saved from answering too many by the #1 Flight Attendant coming back into the galley. She told him he was gonna have to return to his seat so we could finish our work. Thank God! Anyway, they said he was notorious for picking up Flight Attendants on that particular flight. He’d do the same thing about once a month. He’d pull out his BIG money roll to impress the girls. He tried to get my attention during the entire flight but I just stayed away from that side of the plane. The other FA’s made that easy and covered for me since I told them I was in no way interested in whatever ole Reggie boy was offering! He was really Creepy!
- On a very early morning flight from LGA to DFW, we had Ivana Trump. She was wearing this too bright for 6:30 AM hot pink mini-skirt business suit with matching f*ck me heels. Once she was seated, I asked if I could bring her something to drink before takeoff. She asked for Evian. When I got to the galley, I remembered that catering didn’t put Evian water on the plane for the early bird flights. She was already being demanding so instead of telling her, I just filled her glass up with good ole galley tap water. I bet one of the other flight attendants $10 that she’d never know the difference. She slurped it right up like it was the finest spring water on the planet. Every one in the galley was howling by this time because they were all peeking out to watch me deliver it to her.
On this flight, first class wasn’t full and we were waiting at the gate for any late arrivals. At the last minute a man boarded and was seated right next to Ms. Ivana. This gentleman was from Dallas, Tx and his southern accent was as strong if not stronger than my MS accent. From the moment he sat down, she became this helpless female that couldn’t understand a word I said, couldn’t decide what she should choose for breakfast, What did he think she should choose? She would lay her long manicured fingers on his arm every time she said something to him. I got to see the pro in action, boys and girls! You should have seen her work this poor man and he loved it!
I work with Elijah Wood’s brother.
I used to work for Tom Clancy.
I’ve taken meetings with Anne McCaffrey, Orson Scott Card, Douglas Adams, and Dave Arneson.
I once did a private demo for Stephen Spielberg.
I’ve directed Tara Strong, Tom Kane, and Susan Egan.
Plus a whole bunch of miscellaneous encounters, like the time I got trapped in the parking garage at work by paparazzi chasing Brittany Spears.
My wife is related to Ethan Allen
I have a very good friend and one-time fuck buddy who is a cousin of D-list Scottish “celebrity” John Leslie. Nothing very impressive there, but John Leslie dated Catherine Zeta Jones in her early TV career, so that opens up a whole wide world of celebs that I’m three degrees away from.
I particularly love the fact that if you add the fact that Catherine Zeta Jones was in Chicago with Renee Zellweger, that means I’m only five degrees away from the divine Jack White. Tenuous, but it keeps me happy.
My first cousin acted as Hillary Clinton’s personal doctor at a fundraiser during her nomination campaign. So 2.
Lots of science folks and Nobel prize winners are 1 degree or just 2.
Brad Pitt kissed my ex wife. So did Bill Clinton. No tongues though.
Just one. I’ve met Gov. Ed Rendell and I’ve shaken Bill Clinton’s hand.
My husband’s aunt was in the Fleetwoods.
I sold a Creepy Crawler Maker to Smokey Robinson. He was very nice.
My brother has stayed at the home of a friend who lives next door to Vladimir Putin’s stepmother.
A girl I went to high school with seems to work on the edges of Hollywood. She used to work at Sundance and now does something else, but every couple of days a few more photos of herself with celebrities show up on FB. She must have hundreds. I finally got jealous when Nathan Fillion showed up.
I’m two degrees from Jesus incarnate, if you’re a Rastafari that is. My grandfather was surgeon at Haile Selassie I. court, and my mother was introduced to him as well.
Well, Evian spelled backwards is “naive”. 
I shook both Hillary and Bill Clinton’s hands. I’m descended from three Mayflower travelers and related to a couple of Declaration of Independence signers. Otherwise, I got nuthin’.
I got my dining room table from Ethan Allen.
I’ve got a few:
- The dean of my college in grad school is the father of Edi Gathegi. <– He was one of the vampires in the Twilight series of movies.
- I went to high school with and participated in drama shows with Dan Marino’s son. Mr. Marino was a fairly nice guy, but didn’t like the extra attention some of the kids gave him for being famous.
- IIRC, one of my friends’ parents’ friends had a roommate in college whose lab partner went on a date with Ted Bundy. She survived this date due to the luck of having changed her hairstyle and hair color between the day of being asked out and the day of the date. That’s six degrees of separation from me, and a bit distant.
- One of our family friends growing up knew and worked with the guy who crashed the Exxon Valdez.
- We’re family friends with the local consul general for Iceland, and my mother met Vigdís Finnbogadóttir when I was young.
- I went to high school with this guy, who was in the latest Star Trek movie.
- My tattoo artist (and friend) does tattooing work for Tommy Castillo of comic book artistry fame.
There’s probably a few more, but this is what I can come up with off the top of my head. I have more than a few other connections are on the level of “worked with a relative of famous person” or “my relative met famous person while working”.