My first choice in recent films would be Morgan Freeman as Nelson Mandela and Matt Damon as François Pienaar in Invictus (Clint Eastwood, 2009) for the weight of emotion and power of conviction. Even more recently filmed, my next vote must go to Colin Firth as King George VI in The King's Speech (Tom Hooper, 2010) for his authentic emotion and motivation. A third entrant from recent films must be
William Hurt as Professor Willie Esterhuyse and Chiwetel Ejiofor as Thabo Mbeki in Endgame (Pete Travis, 2009) for tapping the authentic dilemma faced by the men negotiating the end of apartheid.

I thought that Dame Judi Dench as Queen Victoria in Mrs Brown was excellent, with just the right balance of regal vulnerability. She also happens to be my favourite Lady Macbeth - despite having few of the qualities I prejudged an appropriate actress to have for the role, she was stunning.

Oh, there are SO many above that I agree with!  (Most notably, I have always adored Blanchett's version in Elizabeth, ... even though the director was constantly yelling at her for spouting how the "real" Elizabeth would have acted!  Ha!)

However, I have to cast my vote for Jim Caviezel as Jesus Christ in Mel Gibson's The Passion of the Christ.  For the first time, a Jesus physically strong enough to make it believeable to withstand the sins of the world, ... while still able to throw His loving arms around his Mother, Mary.

I will second Frank Langella in Nixon. I also liked Al Pacino in Serpico. While the character is Serpico is not someone who was very well known outside of New York, Al Pacino brought him to life and immortalized him. The best impersonations are those that breath new life into a character you've only read about or seen from a distance.

I was amazed by Frank Langella, an actor I don't care for in many of his parts, and the job he did portraying President Nixon in the film Frost Nixon.  He did a fantastic job with Nixon's mannerisms, his voice, even the way he walked and moved.  There were several points in the movie where I forgot I was watching an actor.  Watching the actual Frost interviews also gives you a really good idea of how spot on Langella was in his portrayal of the President.

I was very impressed with the interpretation of Truman Capote made in the movie Capote, by Phillip Seymour Hoffman. I am sure that interpreting someone as complex and unique as Truman Capiote was quite a task for Phillip Seymour Hoffman. In the same movie, Catherine Keener played the character of Nell Harper Lee during the time when she was writing To Kill a Mockingbird. It was surreal to see Harper Lee embodied so well by this actress. Totally loved it! PSH also won the Academy Award for his wonderful acting in this movie!

I have to cast my vote along with Bullgatortail for Richard Burton. He adapted quite naturally to a large number of historical characters. There is no reason for me to repeat the list that he has provided; but can say that I saw all of the movies mentioned--incidentally, I well remember The Valiant Years as a child, but only learned from your post that Churchill's voice was actually Richard Burton. His talent as a Shakespearean actor carried over quite naturally to a number of historical characters. I show a number of his films to my World History classes as he seems to meld into the character he plays.  Kingsley did an excellent job as Ghandi, and Spencer Tracy was a superb actor, but for historical roles, I don't think you can top Richard Burton.

My favorite actor in a historical movie was Spencer Tracy in "Inherit the Wind."  The passion that he brought to the idea of debunking what he saw as backward thinking and, instead, pushing a modernist agenda brought that film to life.  However, he was not actually playing Clarence Darrow but a fictionalized Darrow stand-in named Henry Drummond.  So I suppose that doesn't count.

I suppose I'd name Meryl Streep's role as Karen Silkwood as another that I enjoyed.  I thought she did a really wonderful job of portraying an actual person, but one who was not particularly well-known.  She managed to capture the full personality of the character instead of playing her simply as a heroine.

I also really enjoyed The King's Speech. However, my favourite example of an actress playing an historical figure has to be Cate Blanchett's portrayal of Elizabeth I in Elizabeth. Having studied this period of history myself, I thought her portrayal of a young an vulnerable woman surrounded by various plots, threats and nobles each trying to pursue their own ends was incredibly convincing and revealing. In particular, what stood out most to be was her transformation into the Virgin Queen at the end of the film.

I'm going to give you two from the arts that I really enjoyed:

Jeffery Wright as the street artist Jean-Michel Basquiat in the film Basquiat. Basquiat was discovered by Andy Warhol, but could not survive in the guilded cage of fame. Wright captures the electric personality of the unconventional artist in a way that is both mesmerzing and incredibly sad. http://www.imdb.com/title/tt0115632/

The brilliant, cameleon-like actor Paul Giamatti in American Splendor. This film is narrated by the real Harvey Pekar, who wrote and drew many of the comic books of the same name, depicting the life of his everyday hero, himself. (To see Giamatti's incredible range, catch him in the HBO series John Adams, about the second President of the United States.)

American Splendor: http://www.imdb.com/title/tt0305206/

John Adams: http://www.imdb.com/title/tt0472027/

This is, of course, a subjective question. so perhaps, it can be moved to discussion so that others can comment upon it.  And, it is a difficult question in that one must choose only one movie. 

Two movies come to mind with this question:   The 1970 film Patton starring George C. Scott and Gandhi starring Ben Kingsley.  However, with the question as stated, George C. Scott seems the character who did the best job of impersonation.  Scott, whose performance as General Patton, commander of  in World War II was stellar, actually began to believe that he was General George S. Patton, so much so that he required psychological therapy.  His performance was so authentic that he was asked to perform in The Last Days of Patton,  a made-for-television sequel about Patton's final days after being mortally injured in a car accident.

Scott's performance as General Patton was so realistic because he did much research, studying films of Patton and talking with people who knew him well and because Scott himself had been a Marine from 1945 until 1949.  His family, too, had been military.  His address before the troops, the opening speech of the movie, is highly acclaimed and often studied on its own.  And, the image of Scott as Patton before the U.S. flag has become iconic.

One actor that immediately comes to mind is the Welshman Richard Burton, who was married to Elizabeth Taylor several times. Burton was nominated for seven Oscars during his long career (without ever winning). His distinctive voice, good looks and superlative acting skills became trademarks, and he landed many plum roles, including:

• Prince Hal in an English stage presentation of Shakespeare's Henry IV, Part One.
• Marcellus, a Roman noble who headed the detachment that crucified Jesus in The Robe.
• Winston Churchill in The Valiant Years.
• King Arthur in Camelot.
• The lead role in a Broadway production of Hamlet that was later released as a film. 
• Edwin Booth (John Wilkes Booth's famed acting brother) in The Prince of Players.
• The title character in Alexander the Great.
• Marc Antony in Cleopatra.
• The title role in Becket.
• The title role in Dr. Faustus.
• King Henry VIII in Anne of the Thousand Days.
• The title role in Bluebeard.