Anything from 26 to 35 caliber will cover anything in North America and all but 3-4 animals on the planet. Literally anything from 260 to 35 Whelen. Match your bullet to the game hunted and the only real difference is the effective range, ammo costs and availability, and how much recoil you're willing to tolerate.
Personally I'm sorta a middle of the road guy and settled on 30 caliber rifles years ago, but readily admit the 7mm's are just as good if not better. A 308 or 30-06 would be the 1st choice. For what I do 99% of the time any of the 6.5's will work, but they are starting to be close to borderline for bigger game.
As much as Robert likes his 375 (and I understand the rational), it is just too big for my tastes. It is suitable for the 3-4 other animals referenced above while still being viable for deer size game, I get that. But the way I see it, if I can afford to hunt those 3-4 species, I can afford more than 1 rifle.
And while the 25-06 is a viable deer and varmint round it just doesn't shoot bullets heavy enough to be a good choice for game bigger than deer. I know it's used by some guys for elk, but so is 243. The 25's are only a baby step better than the 24's.