Minecraft wiki entry for Looting, associated text: Mobs with no drops, such as bats, bees, or endermites, are not affected by this enchantment.
Withers, iron golems, and snow golems are not affected by this enchantment.
Looting does not increase the amount of fish dropped by fish mobs (guardians and elder guardians are not considered fish mobs, and Looting does cause them to drop more fish).
Looting does not increase the drop quantity when used on a fox, but it does increase the chance for a drop.
It does not increase the amount of wool dropped by sheep.
The sponge drop from an elder guardian is unaffected.
It does not affect totems of undying dropped by evokers.
It does not affect the amount of skulls dropped by wither skeletons, but does increase the chance for them to drop one.