Number of nominations: Six. Best Supporting Actress in The World According to Garp (1982), Best Supporting Actress in The Big Chill (1983), Best Supporting Actress in The Natural (1984), Best Actress in Fatal Attraction (1987), Best Actress in Dangerous Liasons (1988), Best Actress in Albert Nobbs (2011).
If you think Leo's had a rough go of it, pour one out for poor Glenn Close, who has never won an Oscar despite being nominated in acting categories six times (along with Deborah Kerr and Thelma Ritter, she's the actress with the most nominations never to have won). That's just cruel! It's this sort of stress that leads actors to, say, sleep inside a horse's carcass, or take a role in Albert Nobbs.