Depends where you live, and your experiences. I have lived from New Jersey, to Texas, to Georgia, to New Mexico, to California, to Mississippi, and to Wyoming. I've seen the woods of Appalachia and East Texas, to the Rocky Mountains of Wyoming and the Tetons. The open spaces of the prairies to the swamps of the gulf coast.
Best all around hunting rifle, would have to be qualified. Best for what. If I was told that forgetting local/state laws, and that I was only going to be allowed one rifle/caliber, but I would be allowed to hunt ANY POSSIBLE ANIMAL in the entire North America; from Florida to Alaska.... The answer would be easy.
7mm Remington Magnum.... With 110 grain bullets, you can shoot varmint, coyote, hogs, javalena, etc... you work you way up to shooting moose with 175 grain bullets. It has the flatness of shooting an Antelope or mountain goat at 400+ yards. There literally is not one animal in all of North America, that a 7mm magnum can't effectively shoot.
If you get into the 300 magnums and higher, then they are overkill for many small animals. If you get into the 270/280 and light power than the 7mm magnum, then you give up on the capability of either real long range or taking a very large animal like a Bull Moose. Some will say that there are better again moose; better brush guns; better antelope prairie guns; better all around calibers like 30-06 or 308. There are a lot of reasons to like all of these guns and calibers. And actually, I own just about all of them. But the question was best ALL AROUND hunting rifle. And if the original poster and others truly want the best ALL AROUND, then that has to include Alaska to Maine to Florida to Kansas to Wyoming etc... That would be the 7mm Remington Magnum. Any of the quality rifles in the caliber would be fine. If a person doesn't want to include certain states or certain animals in their hunt, then they can definitely argue a different caliber. But then, they wouldn't be describing the best "All Around". I love my Marlin and Winchester 30-30 lever actions. Excellent for deer hunting in east texas hill country. But that doesn't fall into the category of All Around. The 7mm magnum definitely does. Nothing too small and nothing too big. Not hunting on this continent.