From Terraria Wiki
The Bunny is a background character that cannot harm players. Bunnies have only 5 health, and can be damaged by other mobs including the player, which almost always results in their instant death.
- Corrupting and killing Bunnies appears to make more Bunnies spawn, regardless of whether it is day or night.
- Bunnies spawn near NPCs, causing them to sometimes spawn deep underground.
- The Bunny can be seen on many of Terraria's logos.