I always have binos on me no matter what I am hunting. I absolutely hate it if I ever forget them! For whitetails and closer range game I carry a pair of Vortex 6x32, and for out west or longer range areas I have a pair of Swarovski 8.5x42.
I'll be completely honest - on many hunts, whitetails from a treestand for example, I can't really say they are essential to helping me actually take game most of the time. Usually, what is going to come is going to come, and if they get close enough to shoot I don't really need the binos.
But I really enjoy being able to check things out that are not in range - it simply greatly increases my enjoyment in the field. They really help to be able to see deeper into the brush. And once in awhile I might identify a nice buck that I couldn't have seen clearly otherwise and will then use a grunt call or rattle horns in an effort to bring him closer.
Out west is a whole different ball game, and in that case I really do use them not only to find animals, but to plan stalking routes, etc.
As for how to carry them, I always want them handy. My smaller pair I carry with a chest harness strap that keeps them tight to my chest. My bigger pair I like in a covered bino harness. I've used Badlands, KUIU, and just recently picked up an Alaska Guide Creations harness that I think I will really like.