There are certain items in the game that summon pets when used. They are found randomly in chests, and some are more common than others.

f you want to find them all in single player, the best advice I can give is to open every chest you find. The locations I've listed below were compiled from a month's worth of various Terraria message board posts. They may not be completely accurate, and you may find a pet at a different location.

Cabbage Summons a Guinea Pig. Found in chests near the surface.
Petri Dish Summons a Slime. Found in gold chests. More common in the Dungeon.
Vial of Blood Summons a Bat. Found in gold chests. More common in the Dungeon.
Brain Summons a Zombie. Found in shadow chests. Can sometimes be found in gold chests located near the top of the Underworld layer.
Wolf Fang Summons a Werewolf. Found in gold chests in the wooden structures located in the cavern layer.
Honeycomb Summons a Tiphia (Hornet). Found in gold chests in the lower part of the Underground Jungle.
Note: The Carrot is a PC-exclusive item only available to those who purchased the Collector's Edition of Terraria. It doesn't exist on consoles.