Other than humans, the most intelligent species are primates, most of which are either vegetarian or close to vegetarian, eating meat only occasionally and when the opportunity arises. Some primates hunt, but Gorillas, for instance are vegetarian, as are many others. All are highly intelligent as animals go.
Next to primates, the most intelligent order is Cetacean. There are two types: Mysticetes and Odontocetes. As the name implies, Odontocetes have teeth and are carnivorous, eating fish and squid. This group includes the dolphins, sperm whales, and killer whales, among others. The Mysticetes are also highly intelligent, but they have baleen and are “vegetarian” in that they eat only plankton. Plankton, of course has some animals as well as “plants” (photosynthetic organisms, anyway). So it’s hard to say, exactly, but Mysticetes are generally considered in diet to be the aquatic equivalent of cows.
Of the land animals, elephants are among the most intelligent, and they are vegetarian.