To add to the answers prior to this one:
In the Tiny Tina's Assault on Dragon Keep DLC, at the cost of 2 eridium, you can activate shrines that give you various temporary bonuses: ammo, defense, melee, damage and speed bonuses.
Also, in the TTAoDK DLC, you can give 5 eridium to the queen* after you've rescued her (finished the final story mission).
She can be found in Flamerock Refuge. She has a chance of giving you a weapon whose rarity is either: green, blue, purple, a Hyperion E-tech Dart or Spiker, or a legendary weapon. There is also a small chance that she will produce a health pickup or ammo instead of a weapon.
* By queen, I mean Butt Stallion. And by "giving eridium to the queen" I mean feeding Butt Stallion eridium, and by the queen "giving you weapons/health/ammo", I mean Butt Stallion pooping or vomiting those out. More info here.
In the Ultimate Vault Hunter Upgrade Pack Two: Digistruct Peak Challenge, you can use them to activate 'digistruct' loot chests for 5 eridium.