I think if I were to be limited to just one rifle, and with that, I had to hunt all big game the world over, it would be an impossible task to choose. Of course, if you are going to hunt Africa, which I have done, the minimum caliber in most countries for any of the big five is .375. Now, having said that, here is my short list of my favorite rifles.
For whitetailed deer-my Browning A-bolt hunter in .257 Roberts. At one time I had a string of 17 one-shot kills on deer with it.
For black bear-my Remington mountain rifle in .30-06.
For elk, moose and most African plains game-my .300 Weatherby (Vanguard).
For the big five-my Winchester model 70 Safari Express in .416 Rem. Mag.

Asking one to choose only one rifle is like asking your mechanic to use only one tool to repair your car. JMHO. Besides, I like to buy guns.