Katharine Hepburn has the most Oscars. They're all for Best Actress: Morning Glory (1933), Guess Who's Coming to Dinner (1967), The Lion in Winter (1968), On Golden Pond (1981).
Ingrid Bergman comes in second with three Oscars. Two are for Best Actress (Gaslight, 1945; Anastasia, 1957). One is Best Supporting Actress (Murder on the Orient Express, 1975).
Meryl Streep has two Oscars. One is Best Actress (Sophie's Choice, 1982), and one is for Best Supporting Actress (Kramer vs. Kramer, 1979). At 16 nominations, Meryl holds the record for most nominations for an actor (female or male). Katharine Helpburn had 12 nominations.