A somewhat longer list than many previously posted: 

I'll restrict myself to the major categories.  Here are actors,
actresses and directors who are rumored to have been gay or at least
bi who have won Oscars: 

Janet Gaynor, Sunrise/Seventh Heaven, 1927; Charles Laughton, 1933,
Private Life of Henry VIII; ex-male prostitute Clark Gable, 1934, and
flingee with Marlene Dietrich Claudette Colbert, 1934, It Happened
One Night; flingee with Tallulah Bankhead Hattie McDaniel, 1939, Gone
With the Wind (and if Victor Fleming won Best Director for that, then
George Cukor deserves a piece of it); admittedly bi Laurence Olivier,
Hamlet, 1948 (his competition including Montgomery Clift and Clifton
Webb); Wally Cox's ex-roommate, Marlon Brando, for On the Waterfront,
1954; David Niven, Separate Tables, 1958; AIDS victim Tony
Richardson, Tom Jones, 1963; George Cukor, for My Fair Lady, 1964;
John Schelsinger, Midnight Cowboy, 1969; Brando, The Godfather, '72;
John Gielgud, Arthur, 1981; F. Murray Abraham, Amadeus, 1984;
Bernardo Bertolucci, The Last Emperor, 1987; Jodie Foster, The
Accused and The Silence of the Lambs, 1988 and 1991; Anthony Hopkins,
Silence of the Lambs, 1991.

Finally, there's all-time champ Edith Head, winner of something like
a dozen Costume Oscars.