Give 'em Hell, Harry!
President: Harry Truman
Release: 1975
The Gist: This one man show about the presidency of Harry S. Truman (James Whitmore) was filmed on stage and then released as a film. The title comes from an incident that took place during the 1948 Presidential election when Truman delivered a speech attacking the Republican party. During the speech, a supporter yelled out, "Give 'em Hell, Harry!".
Oscar Count: A sole nomination, but a big one: James Whitmore competed for best actor against the likes of Jack Nicholson (for "One Flew Over a Cuckoo's Nest") and Al Pacino (for "Dog Day Afternoon"). Because he was the only actor in the film, the film technically joined "Who's Afraid of Virginia Woolf?" and "Sleuth" as only one of three films in which entire on-screen billed cast received acting nominations.

"Secret Honor"
"Secret Honor"

Secret Honor
President: Richard Nixon
Release: 1984
The Gist: Robert Altman directed Philip Baker Hall as President Nixon in another one man show based on a play (though filmed separately, as opposed to "Harry!"). A fictional account of Nixon alone in his study, dictating his thoughts into a tape recorder, it was filmed entirely at the University of Michigan, where Altman was a professor at the time.
Oscar Count: Nada.

President: John F. Kennedy
Release: 1991
The Gist: The first of three Oliver Stone films on this list (and inarguably the better one), "JFK" is not about the President so much as it is about the events leading his assassination and the alleged cover-up that followed. Kevin Costner (as former New Orleans district attorney Jim Garrison) leads an incredible cast including Tommy Lee Jones, Kevin Bacon, Sissy Spacek, Gary Oldman, Jack Lemmon, Joe Pesci and John Candy (the President himself is only seen in real archival footage and is not played by an actor).
Oscar Count: The second most nominated film on this list after "Wilson," "JFK" got 8 Oscar noms, including best picture and best director. It won best film editing and best cinematography.

"Jefferson in Paris"
"Jefferson in Paris"
Jefferson in Paris
President: Thomas Jefferson
Release: 1995
The Gist: James Ivory's film is a semi-fictional account of Jefferson's tenure as the Ambassador of the United States to France prior to his Presidency, and his alleged relationships with artist Maria Cosway (Greta Scacchi) and slave Sally Hemings (Thandie Newton). Starring Nick Nolte as Jefferson (and a young Gwyneth Paltrow as his daughter), the film premiered to mixed reviews at the 1995 Cannes Fim Festival.
Oscar Count: None.

President: Richard Nixon
Release: 1995
The Gist: Oliver Stone's fascination with presidents continued with his epic (192 minutes!) depiction of the the political and personal life of Richard Nixon. Starring Anthony Hopkins (controversially, as the studio wanted Tom Hanks or Jack Nicholson) and Joan Allen as Richard and Pat Nixon, the film is -- according to the disclaimer that comes before it -- "an attempt to understand the truth [...] based on numerous public sources and on an incomplete historical record."
Oscar Count: No wins or best picture nod a la "JFK," but four Oscar nominations for Hopkins and Allen's performances, Stephen J. Rivele, Christopher Wilkinson and Oliver Stone's screenplay, plus John Williams' score.