Speaking broadly, the "Oscar curse" tends to affect actors less often than actresses, which I think is likely correlated to the fact that the actress categories tend to skew younger, while the actor categories tend to go older. The average age of Best Actress winners is 35, and bear in mind that that number is arrived at by including Jessica Tandy, who won at 80, and Katherine Hepburn, who won three times after turning 60. Of the 86 winners for Best Actress, 30 of them have been under the age of 30 at the time of their win. By contrast, the average age of Best Actor winners is 44 and only one actor has been under the age of 30 when he won. On average, the winners of Best Actor have had longer to establish themselves before winning and that foundation, in conjunction with the fact that Hollywood tends to value middle aged actors (where it usually disavows knowledge of an actress once she hits middle age), makes Best Actor winners a little less likely to find their careers going over the cliff after winning an Oscar. But that one actor who was under 30 when he won? Yeah, that was Adrien Brody.
Now, admittedly, Brody's pre-Oscar career wasn't so hot that the coldness of his post-Oscar career should be shocking. He started young, appearing as a teenager in Woody Allen's New York Stories and something called The Boy Who Cried Bitch, and then in his early 20s taking small roles in King of the Hill, Angels in the Outfield and Natural Born Killers. Through the mid-90s up until 2002, he appeared in a number of movies most people have never heard of (Nothing to Lose, Solo, Bullet, Six Ways to Sunday, The Undertaker's Wedding, Restaurant, Oxygen, Bread and Roses, Harrison's Flowers, Love the Hard Way and Dummy), as well as a few higher profile films like The Last Time I Committed Suicide, Summer of Sam, and The Affair of the Necklace. And, of course, there was The Thin Red Line.
Legend has it that Brody believed himself to be the star of Terrence Malick's The Thin Red Line while the movie was filming, only to show up at the premiere and find his role had been reduced to something more like a cameo (such is the danger of appearing in a Malick film). So, things weren't exactly on the upswing before he landed his Oscar winning role in The Pianist and there was really nowhere to go but up. Instead he sort of... started going right back down after reaching the Oscar height. His first post-Oscar role was a supporting role (where his credit is as "First Hood") in The Singing Detective, followed by a supporting role in The Village, aka "The Movie Where The Last Holdouts Still Clinging to Fond Memories of The Sixth Sense and Unbreakable Finally Gave Up On M. Night Shyamalan." The forgettable thriller The Jacket followed, which received mixed to negative reviews from critics and grossed less than $10 million domestically. Peter Jackson's King Kong remake came next, which might be considered a rebound because of its success at the box office, but might not be considered a success given that Brody plays pretty much the least interesting character in the film.
From there, his career pretty much follows the same pattern as it did pre-Oscar, with small, little known films like Manolete, Giallo, High School, The Experiment, Wrecked, Detachment and Back to 1942, and slightly more high profile films like Hollywoodland, Cadillac Records, The Darjeeling Limited, The Brothers Bloom, Splice, The Fantastic Mr. Fox and Midnight in Paris. He also starred in Predators which, after King Kong, The Village and Midnight in Paris, is his most financially successful film to date, and this year's InAPPropriate Comedy which, as I understand it, is a sketch comedy movie that's most notable for being worse than the critically reviled Movie 43.
So why didn't winning an Oscar lead to a brighter, leading-man future for Adrien Brody? I'm inclined to say it's the Oscar curse. I mean, an Oscar isn't any kind of guarantee regarding future work, but a Best Actor win should be leverage enough for a few good leading parts, shouldn't it? If the career isn't noticeably better after the Oscar than it was before (except, perhaps, with respect to the paycheque), something went wrong.