The funny part about the big 5, cape buffalo, lions, elephant, leopard, rhino, both black and white, is they are fairly smart, if unperdictible. African elephants have a low frequency language, and can communicate complex ideas. Tava, that Tannin used to have on his website, with myself and my girlfriend riding, is about as smart as a 12 year old, and with that trunk, and size, gets into everything, according to her trainer.
Rhinos, both types, once they get to know you, are easy to scare, but, I think it would be possible to pet one, but I wouldn't exactly make a habit of being around any 10,000 pound animal, just because if they are having a bad day, you startle them, etc. if they lean on you, you are dead.
Cape Buffalo make Madrid fighting bulls seem like domestic cats, with their temper, so, that would be the one I really wouldn't want to try and pet.
Saeed(United Arab Emerites royal family, prince, runs Accurate Reloading website) has already discussed knowing a lion from childhood, and, the lion remembers him, and jumps on him, licking his face, after a long time apart. Lions are social, but, the males have a real fighting instinct, that's impossible to stop, and, you are going to loose, even if they are playing.
Same with leopards. Leopards and lions playing with you could be fatal to your health. Still, it has been done. Segfried and Roy have shown us how close you can get to cats, and, how smart they are.
Keeping any wild animal in captivity is not good for either you, or them, but, still, the above animals are capable of recognizing people, and working with them...
GS