Diablo – What portal do the other goblins have a chance to open/do they open a portal

As mentioned on diablowiki (see Through the Portal), all types of treasure goblins except rainbow goblins have a change to open a portal to the vault.

Goblins not in a Rift will sometimes leave a golden portal behind when they die, granting players in the game access to Greed's Domain, a treasure level full of gold and gems. This portal to The Vault occurs randomly; it is not affected by allowing a Treasure Goblin to live longer, or trying to kill a Goblin just before it escapes through the portal it opens during the combat.

Rainbow Goblins are a special type of Treasure Goblin that may leave open a rainbow portal that takes players to a bonus area called Whimsydale, which is identical in size and layout to the rainbow-themed Whimsyshire easter egg level. Whimsyshire vs. Whimsydale are not the same level -- players who enter this portal and Whimsyshire the normal way in the same game will clear out two different areas -- but the monsters found there and the rewards earned are effectively identical.

As of Patch 2.1.1, the new types of Goblins, the Blood Thief, Odious Collector, Gem Hoarder, and Malevolent Tormentor, may also leave open a golden portal to The Vault just like a normal Treasure Goblin. The secret level is the same in all cases, and the portals opened by the new types of Goblins are the same golden color, though fans have suggested their portals should be palette shifted to match the color of the different goblin types.