Besides "Bad Romance?" Not much.
I've been listening to the deluxe edition of her Grammy-nominated The Fame, and I just can't understand why Lady Gaga has broken out of the club scene to become a genuine pop phenom. Yes, her singles are decent, and she knows how to market herself (and endear herself to the gay community). In that latter sense, she invites comparisons to a young Madonna. But the comparison ends there. Go back and listen to Madonna's first few records. Those songs were some of the best pop of the eighties. Other than the incredible, aforementioned "Bad Romance" (which is as close as she gets to Madge's early brilliance), her material is pretty middling.
So what explains it? Perhaps it's because she's an amalgamation of what people like about other pop stars. She embraces style and fashion (like Gwen Stefani), she's a little outre (like Bjork and Kelis), and she flirts with prurience (like a lite version of Peaches). But is she really greater than the sum of her parts?
I don't think so. I'm reminded of Gertrude Stein's description of Oakland, California: When you listen to Lady Gaga, you find there is no there there.