My great-great grandfather served in the Union Cavalry with George Armstrong Custer (died rather famously in 1876) in the Shenandoah Valley in 1864 and 1865. Not sure if he met him as such, but he certainly would have seen him.
My father served on the El Dorado, the fleet flagship for the battles of Iwo Jima and Okinawa in WWII. Her passengers included the top Navy and Marine brass and Secretary of the Navy Forrestal and war correspondent Ernie Pyle.
I don’t think I’m a direct decendant, but my mother shares her very uncommon maiden name with someone who signed King Charles the First’s death warrant.
My family’s only royal connection that I know of 
Oh, I have also met the Sultan of Brunei’s wives, so I guess that would put me a few degrees away from a lot of heads of state.
I’m a member of the same Howard family that gave us William Howard Taft and all those other (crooked) political Howards. My mother and one of my brothers carry the Howard middle name.
I’m four degrees from General William Tecumseh Sherman (d. 1891). Great grandfather took part in the March to the Sea.
I’d rather talk about my mathematical genealogy. I am 6 degrees from Gauss. I am 2 degrees from Emil Artin and if you follow him on the mathematical genealogy web site (q.g.) you can trace him back 4 generations to Gauss. Seven more generations take me back to Leibniz, who had no known advisor (and presumably no PhD, this must have been a new idea back in the 17th century. BTW, Leibniz has nearly 91,000 descendants. This is a clear majority of the 156,000 people in their database. By contrast, Newton has only 9100 descendants and goes back to Tartaglia (who solved the quartic equation) and stops.
What constitutes a link? A handshake? The person would take your phone call? They autographed a book to you (in person)? You autographed a book to them (in person)? You are Facebook friends? You’ve had dinner together? You swapped stories in a bar or at a conference? They’ve been to your home? I’m never sure how this game is played.
One degree from Benjamin Britten (who was in love with my father) and Albert Einstein.
Einstein puts me two degrees from Charlie Chaplin and every important physicist of the early 20th century.
In my opinion a link means that they actually knew each other. That is, I am only linked to someone if you mentioned me to them and they knew who I am. Briefly meeting a celebrity or being in the same room with them wouldn’t count.
My stepgrandparents were friends with Babe Ruth (d. 1947) because he came into their restaurant at the Grand Concourse in the Bronx.
In the off season, Ellie (Elston) Howard (d. 1980) was the Parks Sausages salesman for Food Fair where my stepdad worked, and they often talked together.
Yogi Berra was the usher at my mother’s church in Hillsdale, New Jersey. He always attended the children’s Mass with them. My mother said he was also very active in the community, and mentored several boys who lost their dads in WW2.
Good post/username combo!
(LBJ was not only no longer President in 1973, he died on January 22 of that year. So it probably wasn’t him, even as an ex-President, unless you’ve got the year wrong.)
I have an antique mantel clock downstairs that was a wedding present from Abraham Lincoln to a relative of mine.
I’m not sure where he was in his career at the time of the wedding. I do know he wasn’t President yet. The family story is that he was asked to give away the bride, a cousin to me (I have no idea how many times removed).
Supposedly, he tucked her arm into his as the wedding march began to play and said, "well, my dear, here we are: the long and the short of it.’
And off she went to get married.
My father met with Gen. George Patton before the North Africa invasion.
I am probably two degrees of separation from Arkansas Governor Orval Faubus, who died in 1994 and is best known for his stand against desegregating the Little Rock high schools in 1957. His grandmother or great-grandmother was my great- or great-great-grandmother. I did meet my great-grandmother and am sure she at least met him sometime during the 20th century. I never met him myself.
I had a friend (who lived to be 99) who, in the 1910s, had interviewed people who’d been there the night Lincoln was shot in 1865.
Three degrees: My mother, aunt, and uncles all remember their great-grandmother, who was (according to family lore) a childhood playmate of John Wilkes Booth (d. 1865).
A cousin of my grandma’s who died last February would call King Juan Carlos Juanito, having known him from childhood. That’s simply the most internationally-known name in her little phone book, along with that Franco guy. Climb “Johnny”'s family tree to reach any big names in Spanish history, plus relatives abroad, plus…
My great-grandfather the cop (who died in 1953, before I was born):
My wife is a shirt-tail relative of Cardinal Tomko (she has a picture of the two of them having a snowball fight from back before he was a big deal and was visting the US), who was tight with John Paul II.
That puts me at 3+x to any Pope, I guess (on the theory that they would have know their immediate predecessor).
The OP asked for the year of the historical figures death. That is why I posted 1973.
Dad talked to LBJ while LBJ was the POTUS.
My father met Barack Obama, so that puts me 3 degrees away from pretty much every head of state alive today, and 4 degrees away from anyone they ever met, so I’m 4 degrees away from any of the famous people that QE2 ever knew, such as Winston Churchill.
Through his son John? John moved to my hometown about 1662 and died here in 1695.