Nominated once, as Best Actress, for Morocco. She was extremely deserving of a Supporting Actress nod for her work in Witness For The Prosecution and, legend has it, was so certain of receiving one that she made room in her stage show to acknowledge the honor that ultimately never came. Surprisingly, she never even received an Honorary Oscar despite being a film legend and despite the considerable amount of time she contributed to the war effort by selling bonds and entertaining the troops.
A classic case of making it look too easy. There's a reason why there's never been another Cary Grant - because it's actually not that easy. He received two nominations as Best Actor for Penny Seranade and None But The Lonely Heart and received an Honorary Oscar in 1970.
It's hard to get too worked up about Garbo's lack of competitive Oscar because from what I understand about her, she probably didn't care anyway. In fact, I have my doubts that she even bothered to show up to collect her Honorary Oscar in 1955. Still, in her short career she turned in several performances that would have been worthy of a win. As it is she was nominated four times as Best Actress for Romance, Anna Christie, Camille and Ninotchka.
One of the first method actors to break into the mainstream, Clift had it all: the looks, the charisma, and the talent. And then the looks were altered in an accident, the charisma started to waver and, in the end, the talent was overtaken by the demons of addiction - Clift may have never won an Oscar, but I bet an actor playing him in a biopic would. He was Oscar nominated four times, thrice as Best Actor for The Search, A Place In The Sun and From Here To Eternity, and once as Best Supporting Actor for Judgment At Nuremberg.
How can Barbara effin' Stanwyck not have an Oscar? She's one of the toughest dames to ever grace the screen, but she could also show a softer side without missing a beat. She was nominated four times as Best Actress for Setlla Dallas, Ball of Fire, Double Indemnity and Sorry, Wrong Number and given an Honorary Oscar in 1982.