To be absolutely accurate, the world's largest deer is Alces alces gigas or Alaskan Moose. There are three other sub-species but the Alskan ies at least 30% larger than any of the others.
By the way Boo, the North American Pronghorn (Antilocapra americana) is an antelope (actually, it's not even a true antelope, occupying a niche all to itself) not a deer, he said pedantly...