For the entire World!
For Cape Buffalo up to Elephant, you'd need something big. You can use a big caliber to let the air out of a grizzly bear if you want too. There are a lot of Nitro Express out there. .416 Rem Mag and WBY are supposed to be big monster killers too, complete with sphincter stretching recoil. I watched a Peter Capstick interview saying he liked the .458 Winchester. It's powerful enough, and you can probably pick up ammo for it anywhere in a pinch. So:
.458 Winchester
For everything from coyotes up to large antelope, I like the 30-06 Springfield. Available all over the World, and you can shoot bullets from 40 grains in Remington Accelerator ammo to what 220 grain bombers. Most people can handle the recoil, and the caliber is inherently accurate. So:
.30-06 Springfield
From everything from bunny rabbits to bobcats... I would never leave home without a .22 LR. If my plane crashed and I had all 3 but could only carry one, I'd take the .22! It's the pot filler. You can carry enough ammo to empty a forest in your shirt pocket, and anyone can shoot it. So:
.22LR
