The majority of non-combat pets drop from the Menagerist Goblin. Obtaining a pet from him is easy — it's a 100% drop for everyone in the party, every time he is encountered. Better yet, it's guaranteed that the pet is not a duplicate. You get a new, unique pet each time.

What does a rainbow Goblin drop?

Rainbow Goblins drop exactly like normal Treasure Goblins, leaking gold and occasional items as they run, and then a loot fountain of gold, items, gems, and materials upon death. They very rarely produce a legendary item, but are good sources of rare items, crafting materials, and gems.

Where can I find pet goblins?

The Menagerist Goblin, Napper of Pets is a variant of the Treasure Goblin in Diablo III, introduced in patch 2.4. 1. It can only appear in Adventure Mode, usually in open world (but on rare occasions, can spawn in Nephalem Rifts as well).