We’ve all heard the sentiment, or some version of it, uttered during the Oscars: It’s an honor just to be nominated. And who knows — in some cases, it might even be true. But in the end, when it comes to the acting honors, there’s only one person up there on the stage, hugging (or, if it’s a guy, holding high) that inimitable golden statuette. In those prestigious individual categories that take the spotlight near the end of the night — director, for example, and the supporting and lead actors and actresses — there’s the winner, and then there’s all the rest.

Here, LIFE.com celebrates Hollywood legends — and a few stars who, while huge in their time, have dimmed with the passing years — as they bask in the limelight, marvel at their good fortune, sit as if dazed by the honor bestowed on them and, in a few instances, go about their lives as if nothing had happened (albeit with an Oscar statuette somehow miraculously within reach). Here are Taylor, Crosby, Hepburn, Brando, Joan Crawford, Grace Kelly, Jimmy Stewart and other actors and actresses who have won at least one Oscar — many of these folks, of course, won more than one — spending some quality time with that most coveted of moviedom’s trophies.

Here’s to the winners.