Bats are common flying enemies. They follow the Bat AI, randomly flying around and bumping into things while trying to make contact with the player.
Pre Hardmode Bats:
Cave Bat: Common Cavern/Underground enemy
Jungle Bat: Common Jungle enemy
Hellbat: Common Underworld enemy
Ice Bat: Common Underground Snow enemy, inflicts Chilled and rarely Frozen on impact
Hardmode Bats:
Giant Bat: Common Cavern enemy, inflicts Confused on impact
Illuminant Bat: Common Underground Hallow enemy
Lava Bat: Common Underworld enemy
Slimer: Corruption enemy, changes form into a Slime when health is depleted
Giant Flying Fox: common Jungle enemy, only spawns at night in place of Derpling
Vampire: Solar Eclipse enemy, pursues player as bat and changes into humanoid form when near.