My starting point is I know one person who has killed a mouse barehanded... That makes mice and rats long odds in my book for me. Anything else on that list, I wouldn't bet a candy bar on me personally, as I have seen way too many human/animal interactions that were along the lines of
@EddieWalker's. That said, with the possible exception of polar bears, and pigs, most animals aren't in it for a fight to the death. Escape is top of mind.
I have an acquaintance who can kill rattlesnakes barehanded by grabbing their tails and snapping them once like a whip. I would not have believed it possible if I had not seen him do it multiple times. It is 100% technique; his reflexes are not fast. And no, I'm, never, ever, trying that myself. I lived for a time where the cobras had local names that were basically the number of steps you could take after being bitten, seven, eleven, fourteen, and twenty one.
I do better with a tool.
I'm sure many of you are more talented.
All the best,
Peter