No matter the wilde game there's an ammo caliber designed for it.
Benchrest target shooters strive for tiny groups measured with a micrometer rather than a ruler. Their caliber of choice is the 6mm PPC, based off the .220 Russian. The PPC is still new as far as cartridges are judged and it knocked the .222 Remington or triple deuce from the benchrest podium soon after its introduction in 1975. Recently several calibers including; the 6mm BR and 30 BR, have made a charge at the PPC kingdom and I wouldn't be surprised to see it fall, but for now its reign is safe.
"Across the Course" matches or NRA Highpower with its roots derived from the military, depends heavily on military based rifles and calibers.
Therefore, the 5.56 and 7.62 NATO are two of the most popular cartridges, but there are others.
Shooting legend, David Tubb is never satisfied until he squeezes the most from a cartridge. He developed a cartridge of his own by simply short chambering a standard .243 Winchester then necking 22-250 brass to fit the new chamber. After some refinements, Tubb settled on the current version known in the shooting world as the 6XC. Its closest competition, the 6mm Dasher, is another across the course favorite.
Longer ranges call for more powder and longer bullets — 1,000-yard shooters need both to remain competitive. Like most target shooters, long range shooters use custom rifles designed especially for 1,000-yard shooting, including custom barrels to stabilize these heavy bullets. Favorite calibers include the 6.5-.284, 6mmDasher 6mm BR and the .30 caliber magnums.
On the hunting side of rifle caliber choices, there are too many to list, but some thought should go into the caliber to hunt big game. Personally I'm a traditionalist and prefer a bigger diameter bullet with plenty of speed and great bullet selection. The .30 caliber short magnums are often my preferred choice, but I have been lusting at the .300 Remington Ultra Magnum (RUM) for quite a while and might have to break down and get one soon.
As a "gun guy", I'm often asked by parents of first time hunters if the .223 or .243 Winchester is enough gun to hunt deer. My answer is always same: "Yes, if they can shoot it well."
A small well-constructed bullet put in the right place is much more lethal than a .338 Loudenboomer through a non-vital area. Of course, the best of both worlds would be a well-placed bullet with sufficient weight and construction to dispatch the animal quickly, but hunting doesn't always go according to plan. The old adage of hope for the best and expect the worst is a good rule to keep in mind when choosing a caliber.
I have taken deer with a .223 (a grand total of one) and used many other much larger calibers. The deer had no clue what I was using and the effect was exactly the same; fresh venison, but I still don't consider the .223 Remington an ideal deer cartridge nor do I think the .300 RUM is one either.
But, when conditions go south, distances are long and its 4th and goal, I want enough gun to get the job done.