When we talk about cartridges being versatile, and this cartridge for this animal or that animal we need to look at classes or groups of cartridges. Here is a very partial list.

varmits:
.22 hornet
.223 Rem
.22-250 Rem
.220 Swift

deer/coyote dual purpose:
.243 Win
6mm Rem
.25-06 Rem
.257 Roberts

deer/caribou/elk/moose 250yd-300yd

.260 Rem
6.5x55 Swede
7mm-08 Rem
.308 Win

deer/caribou/elk/moose 350yd

.264 Win Mag
.270 Win
.280 Rem
30/06

elk/moose at ranges longer than most should shoot

7mm mags
.300 mags
.338 mags

Big dangerous game that can kick the s^!$ out of you if you wound him

.358 Norma Mag
.375 Mags
.416mags
.458 mags