I haven't seen too many animals in the wild but have managed to run into: black bear, roosevelt elk, moose, bison, deer, loon, blad eagles, coyotes, bobcats, marmots, and umm... cattle.
While hiking in Africa (no cars) I've run into elepants and water buffalo. Hiking into an elephant herd when your group doesn't have a radio or guns (to frighten them off) turned out to be pretty exciting as we ended up climbing some trees and hoping the elephants wouldn't attack us while others tried to scare them off the trail with sticks and yelling. These weren't domesticated elephants and can kill you easily if they're upset (why we were in the trees). If you go to Africa, visit some some places on your feet instead of in SUVs
I still want to visit Yellowstone in the winter sometime and see the bison then.