Nebraska

Nebraska offers some interesting hunts, including Rocky Mountain Bighorn Sheep (residents only, and only offered when the population is doing well), elk (residents only), antelope (essentially residents only, except for archery tags), and mule deer.

But, for practical purposes, what Nebraska really offers is great whitetail and turkey hunting. Tags for both are very easy to come by, and limits are very liberal compared to any other western state.

For bird hunters, duck and goose hunting is excellent, if you can find a place to hunt. There's also great pheasant hunting, again, if you can find a place to hunt.