The single most famous instance of "Whaddaya got" in U.S. popular culture is probably the exchange between Mildred (Peggy Maley) and Johnny Strabler (Marlon Brando) in The Wild One (1953):
Mildred: Hey Johnny, what are you rebelling against?
Johnny: Whadda you got?
That spelling is the Internet Movie Database's, by the way—Brando doesn't pronounce the "you" as "yoo"; in fact, he pronounces "Whaddaya" more like "Wudduhyuh."
The spelling "What do you got" remains somewhat uncommon in Google Books results and goes back only to about 1990, though both Philip Roth (in I Married a Communist  and The Plot Against America ) and Tom Clancy (in Rainbow Six  and The Bear and the Dragon ) have used it more than once. I've also noticed that in a popular U.S. comic strip, Pearls Before Swine, the cartoonist sometimes sets up a joke in the first panel by having one character ask another, e.g., "What do you got there, Rat?" It looks odd to me. I'm fairly sure, though, that usage of "What do you got" in written U.S. English has increased significantly since the turn of the century.
The first written instance of the phrase that I've been able to find is in a joke from 1915, and the spelling used is "whaddya got." From The Judge, volume 68 (subsequently reprinted in scads of periodicals over the next decade, and as late as 1960 in The Complete Toastmaster: A New Treasury for Speakers):
Tourist (in village notion store)—Whaddya got in the shape of automobile tires?
Saleslady—Funeral wreaths, life preservers, invalid cushions, and doughnuts.
They sure don't write 'em like that any more.