I have one nomination at the tip of my tongue:
Eugene Levy was born to play Vince Lombardi.
How many other instances like this can we come up with? Extra points if said performer actually DID play the famous person in a movie or TV program.
George C. Scott for his potrayal of Patton.
Marc
Elijah Wood as Frodo Baggins. Helps that Bakshi drew Frodo to look exactly like him.
Patrick Stewart as Charles Xavier.
Sorry, all. When I said “famous people”, understand that to mean “famous people who actually exist(ed), as opposed to fictional characters”.
Ed Harris as Jackson Pollock.
Harris tells the story that his father sent him a copy of a Pollock biography because of the eerie similarity between the photo of Pollock on the back of the book and Harris. After reading the book, Harris put the wheels in motion for what eventually became the film. Harris was outstanding as the troubled artist.
Pash
Ed Harris as Jackson Pollock
Val Kilmer as Jim Morrison
Al Pacino as Sonny Wortzik
I think they were all better playing the actual person than the actual person was at playing themselves.
To a lesser extent, Geoffrey Rush as David Helfgott.
I don’t know his name, but he played the asshole news guy in Die Hard. If there’s ever a TV movie about David Duke, this guy needs a phone call.
Well, obviously, Stephen Fry as Oscar Wilde
Gary Oldman
as Sid Vicious in “Sid & Nancy”
as Joe Orton in “Prick Up Your Ears”
as Lee Harvey Oswald in “JFK”
This isn’t nearly as famous, but when Billy Crystal’s HBO move “61*” came out a few months ago, a lot of people commented how Barry Pepper looked exactly like Roger Maris facially, and had really gotten the swing and other playing habits down, too…
And although Charles Xavier isn’t real, I have to agree that the only person for the part was Patrick Stewart
Another obscure one: Ian Hart as John Lennon in “BackBeat” about the Beatles when Stu Sutcliffe was a member and they were in Hamberg - good movie.
Hal Holbrook as Lincoln - he did a one man show some years ago and did an amazing job…
Martin Short as an elderly Katharine Hepburn - she’s my favorite actress and I can barely tolerate him, but it’s pretty damn funny…
Christina Taylor was born to portray Maureen McCormick.
William Devane as John F. Kennedy (I think he played Kennedy once in a TV movie). He has that “Kennedy” look. Put an extra hundred pounds on him and he could play Ted. 
Tammy Blanchard as Judy Garland. She played the young Judy in the recent miniseries, with Judy Davis as the older version.
Caracticus, you’re thinking of The Missiles of October. As far as I’m concerned, William Devane is John F. Kennedy, and Martin Sheen is Bobby.
Terrible film! 
We had to watch it in Civics in high school. Martin Sheen had me rolling with his overracting (usually incredible). The problem with JFK (and Bobby) is that most people play them as stereotypes. Charictures instead of characters. That’s what I liked about the guys in 13 days. They played the guys as REAL characters. They did the accents, but it wasn’t a bunch of “ums” and “ers”. Most people sound like Diamond Joe Quimby when playing the Kennedy’s.
David Hyde Pierce as young Truman Capote.
Casey Kasem as Shaggy on Scooby Doo
Ben Kingsley as Ghandi
Shelley Duvall as Olive Oyl
Ian Hart also played Lennon again in The Hours and the Times.
Leelee Sobieski as Helen Hunt.
I can’t agree more… he was absolutely perfect as Sid Vicious and there isn’t another actor who could have done it as well as him. Actually, I believe Gary Oldman to be one of the finest actors we have today.
Ronnie Wood (of the Rolling Stones) as Charlie Callas