Really, just about any of the 30-ish caliber battle rifle cartridges including .30-06, .308/7.62x51, .303 British, 7.92x57 Mauser, 7.62x54R, .30-40 Krag, 7.5x55 Swiss, 7.5x54 French, 7.7 Japanese, 7.65x53 Argentine Mauser, 8x56R Steyr-Mannlicher, and even 7.35 Carcano and 8x50R Lebel would be sufficient for any North American Game if loaded with the right bullet. Some of the smaller-bore cartridges including 6.5 Carcano, 6.5 Arisaka, 6.5 Swede, and 7mm Mauser would also be fine for most North American game although I'd be a bit hesitant to use them on grizzly due to limitations in bullet weight.