Without even acknowledging the existence of short mags, super short mags, super duper short mags, or super duper pooper short mags (the SDPSM), this is my list of personal favorites.
1) .22-250 is probably the best all around in my humble opinion.
2) .243 a close second, but could arguably be tied for the best.
3) .300 Win. Mag, the best if fur is of zero concern. (They don't even twitch)
4) .223 adequate and fun, especially in a carbine length AR, for tighter areas. I've had a few more run offs with .223, but they still died nearby.
5) 12 gauge - The undisputed king in close cover.
Also .220 Swift is probably up there, although I have no personal experience with it.
There, glad I could settle that once and for all.