Vases appear in Subcon during Super Mario Bros. 2. In that game, they seem to replace Warp Pipes; if a character goes down a vase, he/she will appear in a small room sometimes containing a key. Vases made a small appearance in the Super Smash Bros. Melee course Mushroom Kingdom II, which also took place Subcon.
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. This boss was referenced in Yoshi's Island DS (which also included Super Mario World 2: Yoshi's Island-style pots) through the Potted Ghost enemy. Pots also cameod on Incoming Chomps' platforms in Super Mario Advance 3: Yoshi's Island, though they were not there in the original game.
In Yoshi's Story, Vases are smaller and more round and like those of Super Mario Bros. 2, act more like Warp Pipes. Vases made a minor appearances 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.