After asking my wife, from Texas and with ancestors from swamp country in Louisiana, she says the only "varmint" you need one of those for is the two legged variety, coming in varieties such as ex-husband and get the heck off my lawn.

Varmint needing more than a squirrel gun includes gator, for which she recommends a shot-gun.

EDIT: after seeings Gryphons post, I'll add that shooting milk cartons and such like is a perfectly good excuse, and more people should adopt it.