Diablo III: Reaper of Souls

Treasure Goblins are these small annoying creatures that will run away once you engage them and will drop a huge amount of loot if they are killed before they jump into their portal (if you take too long to kill it). They are not that common, but you should encounter quite a few during your first playthrough. There is also another way to get a good chunk of these out of the way, which is by doing rifts. Rifts have a chance of actually spawning a whole pack of goblins (I've seen a total of 10 packs (50 goblins) in the same Rift), but this is something that can be extremely rare. Your best bet is to find them in the Rifts though.
If you are on PS4, you can follow this tip by homerjrnick:

" A good way to get goblin kills is to get into the goblins lair called The Vault. This was a random portal that appeared after killing a goblin but you can now force open the portal. Simply get the Kanai Cube from Act V and you get a new artisan in your town. Interacting with the cube gives you some options but if you have a Puzzle Ring in your inventory of your character then the first option will be "???" and will consume the Puzzle Ring...if you do this then it opens a portal to The Vault where you will encounter something like 5 goblins. "