Reposted from a similar 2010 thread.
I have either killed or witnessed the killing of maybe 40 deer, with everything from service pistol calibers (above 9mm) through the classic bigbore revolvers, centerfire rifles from .223 through 45-70. Oh, 12 and 20 gauge slugs, too.
FWIW the only 'instant kills' I have seen have been when the bullet destroyed the spine at the shoulder- as in 'wrecked it' and sailed on through. Didn't matter if it was a 240 grain .44 SWC at 1000 fps, 150 grain softpoint from a 30-30 at over 200 yards- or a 175 grain softpoint from a long-barreled 7mm Mauser. Didn't matter if the deer were standing still or in a flat-out sprint. Bang. Flop. Skid.
Shots that took out the shoulder bone (front of the shoulder on whitetail) anchored them almost as fast, though a finishing shot was sometimes required. Broadside heart shots generally elicited about a 20 yard trot followed by a flop.
Worst shot I ever made was on a doe that goosed just as I pressed off a 300 grain .44 XTP at 1350 fps, and it landed about halfway down the back under the spine. That one was a 250 yard tracking job with a dead deer at the end.