I've thought about this a lot lately and now think the following would cover a lot of hunting:
.22 LR - target practice, grouse, rabbits.
.223 Rem - varmints, longer range target work
.270 Win - pronghorn, deer, mountain goats, sheep, elk
.375 H&H Magnum - bears, moose, buffalo, the occasional African safari

12 gauge - skeet, trap, ducks, upland birds
T/C Encore in .22 LR, .270, .375 H&H and 12 gauge as a backup for all.
That's a four rifle battery and a shotgun, with a backup that covers everything. So six guns in total.
But of course, that's if you don't target shoot in any specific disciplines. Doesn't cover handguns or black powder either. It's also inadequate if you want to own and use a variety of different guns for interest's sake. Some of us like trying out old Lee Enfields, or we want a gun in each action type to experience them all. Or we want a beater and a safe queen in each caliber. There are also guns which are great for specific applications but not ideal for others. If you want to go on walkabout with a lever gun in a pistol caliber, then by all means get one. The hunting rifles would cover you but none are so uniquely adapted for small to medium game to black bear defense when you just want to fish rivers and streams. If you want to hunt the bush with a .30-30 or a .45-70, then get one! They are sweet handling little rifles with modest recoil. AR for a tacticool target rifle? Knock yourself out. Handguns differ for Olympic Pistol, IPSC, PPC, IDPA, IHMSA, etc etc. Double barreled shotguns could be owned specifically for Skeet or Trap, etc.
So own the best guns you can afford to do everything that you want to do, and maybe think about keeping it down to that.