Well at the Cincinnati Zoo I have only touched the animals brought out by the docents, the children's zoo animals (I have a soft spot for the two Dexter Cows ), scratched a giraffe's chin while feeding it at the feeding station, and during a special over-night experience in Manatee Springs while behind the scenes above the manatee exhibit a manatee did rub up against my hand. All of this was under keeper supervision. I wouldn't be one to go and touch the animals at the zoo without permission or supervision of the keepers.
Though at an exotic animal ranch and children's zoo in Centerville, Ohio you are allowed to touch and feed(Very few are you allowed to) certain animals. There I've touched and fed a young Nilgai bull, a Chital doe, Fallow Deer, a Yak calf, two Water Buffalo calves, a Red Deer cow, ostriches, emus, a Bornean Bearded Pig piglet, Blackbuck, and a Grant's Zebra, along with the regular children's zoo animals. All was under docent supervision.