I think it depends on the kind of wildlife photography.
I think most people do handheld since it's the simplest option, but that would mostly be for situations when you're rather mobile and you're constantly on the move.
Monopods tend to be used by those guys who have big and heavy equipment. The sort of stuff that's... probably out of most people's price ranges. Usually the monopod acts as a kind of load bearing thing, while at least giving some stability (mostly made irrelevant these days by advanced image stabilisation, usually optically).
I've rarely seen tripods in use for wildlife photography, though usually the reason for it would be if someone set it up in some kind of hide. The objective here is that you're watching some watering hole, or observing a burrow, and you're hidden in a hide with camoflage, and you're probably waiting hours for the animal to turn up, but the idea is that once the animal does turn up, your camera is already in position and angled at the shot you want to take.
I've almost never seen bird photographers use tripods. I've sometimes seen them use monopods for their big chungus telephoto lenses, and most just seem happy with handheld.