I've killed birds and squirrels with slingshot as a kid. Nothing bigger. I always use marbles too for ammo in slingshots. BB's work pretty well too, but much harder to hold and aim with.

I've killed skunks with the 1000fps airguns. Among other various critters. On the bigger animals like skunks and raccoons, good clean headshots is the only way. Too much fur to penetrate other body parts.