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Vases first appeared in Subcon during Super Mario Bros. 2. Vases are objects originally from Planet Earth.

Super Mario Bros. 2
In Super Mario Bros. 2, they are the main modes of transportation of Subcon, similar to that of Warp Pipes from Mushroom World and the Real World; if a character goes down a vase, they will appear in a small room sometimes containing a key being protected by a Phanto. In some levels throwing a Potion on to a vase will allow the player to warp through the Worlds, acting as the Warp Zones of Super Mario Bros. 2. Potions wont work inside vases though. Cobrats sometimes lurk in the opening of some vases. Certain vases generate endless streams of enemies like Bob-ombs or red Shy Guys unless their entrances are blocked. Vases made a small appearance in the Super Smash Bros. Melee course Mushroom Kingdom II, which also took place in Subcon. Some Vases also contain Balls

BS Super Mario USA
Vases also appeared in the pseudo-sequel, BS Super Mario USA, and can be used in the same way as Super Mario Bros. 2. In Subspace, Vases will lead Mario to Wart and they shall battle against each other.

Mario Kart 7
Vases appear as background items throughout the Shy Guy Bazaar course in Mario Kart 7. They maintain their original appearance and coloration from Super Mario Bros. 2. If driven into, they break and some items will fly out, namely Bananas. Some of them can also walk and move around, and they reveal many snakes when broken.

Super Mario World 2: Yoshi's Island
Vases of a much different kind later appeared in Super Mario World 2: Yoshi's Island, here called Pots. These pots were about Yoshi's size, and were often found in castles and would reveal contents (usually a key) upon breaking after a fall. One of these pots was even "powered up" by Kamek, forming Roger the Potted Ghost. Pots also made a cameo on Chomps' platforms in Super Mario Advance 3: Yoshi's Island, though they were not there in the original game.

Yoshi's Story
In Yoshi's Story, Magic Vases make an appearance.

Yoshi's Island DS
Roger the Potted Ghost was referenced in Yoshi's Island DS (which also included Super Mario World 2: Yoshi's Island-style pots) through the Potted Ghost enemy.

Other Appearances
Vases made a minor appearance as a part of Virtual Boy Wario Land's vase-based enemy.

Mimi once had a vase in the game Super Paper Mario but when Mario broke the vase by accident, Mimi said he owed her 1,000,000 Rubees. Mario eventually got them. An exact replica of Mimi's vase can be seen in the house of Heronicus in Flipside in Super Paper Mario.