Cary Grant never won a competitive Oscar. There's one. If you want to take it by nominations with Nicholson you can even bo back to the 1960s as he was nominated for Easy Rider.
ALFRED HITCHCOCK (the renowned "Master of Suspense") never won a single award for Best Director - not even when his film "Rebecca" (1940) was voted Best Motion Picture... Among the film profession, many (who ultimately also do the voting) found the Master difficult to work with.
Famous actors who have never won an Oscar include JAMES DEAN (who d.1955 just after completing "Giant"), and HARRISON FORD (despite starring in 6 of the top 10 highest grossing films by 1989 - the "Star Wars" trilogy and the "Indiana Jones" trilogy). However the record for most nominations without a win is shared by two actors, RICHARD BURTON and PETER O'TOOLE, each with seven nominations (a record shared with Geraldine Page until she finally won an award in 1985).