Teresa Wright did it in 1942 I believe - The Pride of the Yankees and Mrs. Miniver - she won for Mrs. Miniver
Jessica Lange in 1981 - She was nominated for Frances and Tootsie - she won for Tootsie.
Sigourney Weaver did it in 1988 - Gorillas in the Mist and Working Girl, she lost both.
Al Pacino in 1992 was nominated for Scent of a Woman and Glengarry Glen Ross - he won for Scent of a Woman
Holly Hunter did it in 1993 - nominated for The Piano and The Firm - won for The Piano
Emma Thompson also did it in 1993 - The Remains of the Day and In The Name of the Father - she was shut out.
Julianne Moore in 2002 was nominated for Far From Heaven and The Hours - she lost for both.
Jamie Foxx did it in 2004 - he won for Ray but lost the supporting nomination for Collateral
FINALLY -
Cate Blanchett was nominated twice in 2007 for Elizabeth - The Golden Years and I'm Not There where she played Bob Dylan, she lost both.
I'm kind of an Academy Award geek!!!