Fellow Actors
Many actors have been nominated for portraying real people; there is a tiny subset of actors who have been nominated for portraying other Oscar nominated actors:
Robert Downey Jr. as Charlie Chaplin
Downey received a Best Actor nomination for Chaplin (1992), a biopic of the silent film auteur. Chaplin himself was nominated twice as Best Actor, for The Circus (1928) and The Great Dictator (1940.)
Cate Blanchett as Katharine Hepburn
Blanchett won the Best Supporting Actress Oscar for The Aviator (2004), the Howard Hughes biopic that portrayed his romance with Katharine Hepburn. Ms. Hepburn holds the all-time record for most acting victories, winning her very first nomination for Morning Glory (1933), her very last nomination for On Golden Pond (1981), plus two consecutive wins for Guess Who's Coming to Dinner (1967) and The Lion in Winter (1968); she also received eight more Best Actress nominations.
Kenneth Branagh as Laurence Olivier
This year's film My Week With Marilyn depicts the shoot for the 1957 film The Prince and the Showgirl. Kenneth Branagh is nominated for portraying the film's director and star, Laurence Olivier. Sir Larry received 10 Oscar nominations for acting in his long career, winning for Hamlet (1948).
Branagh and Olivier share another piece of Oscar trivia; they both received Best Actor nods as Shakespeare's Henry V, in their 1946 and 1989 adaptations.