Generally, I'd go with 35cal. and above for "knockdown" power - 358Win., 350Rem.Mag,
or 35Whelen. However, I have knocked 'em off their feet with smaller calibers also.
The first I recall was a mule deer doe, uphill shot, lung hit just behind the shoulder with a 308Win., 150gr. soft point @ approx. 125yds. She hit the ground so hard she literally bounced. Kicked a few times, and that was all. The bullet had angled upward, and the wound channel came within a couple inches of the spine. I've dropped two others in their tracks with 308Win., 150gr. also - one at 30yds., other at approx. 50yds.
Another was a 7mmRem.Mag. used on a BIG buck mule deer. Again, an uphill shot.
My friend shot, and the buck HIT the ground. Again, a few kicks, and that was it. Never
took a step.
Another friend used a 260Rem. on a whitetail last year (level ground - no up/down angles), and the doe dropped in her tracks.
My 358Win. is my favorite though, for whitetails. I use the Win. factory 200gr. loads. One hit behind shoulders, and dropped in it's tracks. Another was hit front facing. It ran
approx. 20yds., and dropped. A third was hit, and ran about 75yds.+/-. Of course, the bullet had cut down a 2" diameter tree enroute to the deer - never seen tree, guess it
was "covered" by the verticle crosshair in scope. Guess the tree took a little steam out of that one before it hit the deer.
Given a reasonable caliber, good bullet of decent weight, it mostly just depends on good shot placement, and if the animal is alerted/pumping any adrenalin or not.