It is a pretty commonly held belief that the .375H&H is the most versatile caliber you could own and as the legendary Jack O'Connor said, "If was limited to only one rifle to hunt the world, it would be the .375H&H." (I think he liked the .270 Win when limited to North American game)
It is the standard in Africa, and the smallest legal caliber for thick skinned game in several African nations. A large part of its versatility stems from the range of bullets available. 300 grain loads are standard for thick skinned game... 265gr to 275gr is great for bears of all type... and a personal favorite of mine is the 235 grain, which I use on deer and elk. It has a muzzle velocity of 3,000fps and shoots about as flat as a .270. I took a pronghorn at 500 yards. If you handload you can also try 210 grain and 350 grain, at either extreme. While people will say that it is overkill I simply ask, "how dead is too dead?" In my experience there is very little meat damage, in most cases less than with smaller calibers. It is great fun to shoot. Makes a helluva racket at the range. The recoil has more bark than bite. Ammunition is readily available. And here in the States, you will probably be the only one with it in deer camp.
A word of advice, however... if you get a dangerous game caliber like the .375H&H, get a rifle with controlled round feeding. At least if you actually intend to hunt dangerous game. I will get a lot of flack from Remington M700 fans, but in my five trips to Africa I have yet to hunt with a PH that relied on a push feed action.
So much for my primer on the .375H&H.