I've killed lots of deer, hogs and coyotes with many cartridges form 223 Rem (neck shots deer, head shots hogs, coyotes) to 338 Win Mag. I have multiple rifles in most of the common factory offered cartridges from 223 Rem to 375 H&H Mag. 7mm-08 Rem, 308 Win and 30-06 are my three favorites with 300 Wing Mag, 7mm Rem Mag and 6.5 Creedmoor, right on their heels. 338 Win Mag and 375 H&H are used in areas where brown bear may be present.
In 7mm-08 I use 160gr to 168gr C&C or 140gr TTSX solids. 308 Win gets feed 165gr to 178gr C&C or 130gr to 150gr TTSX solids. In 30-06 I use 180gr C&C or 165 to 180gr TTSX solids.
I've taken deer with the 308 Wins at over 400 yards with no problem. The only reason I haven't killed them farther with it, is because I use my other, more powerful cartridges in places where longer shots are more likely to prescient opportunity.