In my opinion, anything less than a 44 mag, you may as well just throw the whole firearm at them.
I have to agree with John on this matter... The only critter out there that gives me pause, and cause to carry, would be Bears. (or perhaps a Mountain Lion, but if one of those are after me, I give up! )... If the caliber doesn't start with the number 4 (in a handgun) against a bear your kidding yourself. Lighter caliber's (even a 357 mag would be a "maybe", simply cant penetrate a bears bone & musculature...and continue on to deal a death blow. at least on grizzers.... That's how they got their name!
The Lewis & Clarke expedition, upon their encounters with them found their firearms to be insufficient to bring one down...
The Indians warned Lewis and Clark about the Grizzly Bear, which they never attacked unless they were in a party of six to eight men. Here is an account of a Grizzly encounter in Lewis's own words having spotted a grizzly 300 yards away.
"…they took the advantage of a small eminence which concealed them and got within 40 paces of him unperceived, two of them reserved their fires as had been previously conscerted, the four others fired nearly at the same time and put each his bullet through him, two of the balls passed through the bulk of both lobes of his lungs, in an instant this monster ran at them with open mouth, the two who had reserved their fires discharged their pieces at him as he came towards them, boath of them struck him, one only slightly and the other fortunately broke his shoulder, this however only retarded his motion for a moment only, the men unable to reload their guns took to flight, the bear pursued and had very nearly overtaken them before they reached the river; two of the party betook themselves to a canoe and the others seperated an concealed themselves among the willows, reloaded their pieces, each discharged his piece at him as they had an opportunity they struck him several times again but the guns served only to direct the bear to them, in this manner he pursued two of them seperately so close that they were obliged to throw aside their guns and pouches and throw themselves into the river altho’ the bank was nearly twenty feet perpendicular; so enraged was this anamal that he plunged into the river only a few feet behind the second man he had compelled take refuge in the water, when one of those who still remained on shore shot him through the head and finally killed him; they then took him on shore and butchered him when they found eight balls had passed through him in different directions."