Jellyfish

Jellyfish are giant water-dwelling creatures that live around Yoshi's Island. They are invincible to all known means of defeat, and have a greed for intruders to their waters. Jellyfish come in Blue, Red, and Green. Blue Jellyfish simply move up and down. Red Jellyfish chase Yoshi. Green Jellyfish simply float in place. Red Jellyfish can sometimes have an item like a Fruit or a Heart Fruit.

It is entirely possible that Jellyfish are related to Jelectros, another type of jellyfish enemy found in Super Mario Bros. 3. Pre-Yoshi's Story jellyfish also appeared in Super Mario World 2: Yoshi's Island, going under the name "Preying Mantas".

Mario & Wario
In Mario & Wario, Wario uses a jellyfish on one stage to obscure Mario's view.

Yoshi's Story
In Yoshi's Story, Jellyfish only appear in the level Lots'O'Jellyfish!. Green ones don't appear until the third part of the level.

Mario & Luigi: Superstar Saga
There are also two Jellyfish Sisters in Mario & Luigi: Superstar Saga. In this game, Jellyfish are depicted as a humanoid, Toad-like, bipedal, and very rare species. As a matter of fact, only two other Jellyfish exist in the game, one as a clerk in the Massage Room, the other at the beach of the Beanbean Kingdom explaining how to cross Oho Ocean.

Donkey Kong Jungle Beat
Later in Donkey Kong Jungle Beat small Jellyfish that looked more like actual ones and not cartoon-like ones appeared as enemies that would shock Donkey Kong.

Super Mario Galaxy
In Super Mario Galaxy, Jellyfish appear in various galaxies, mostly in the Deep Dark Galaxy. They float arround the water and they would hurt the player when touched. They can be defeated by Star Spinning them and the huge one can in Deep Dark Galaxy can be desimated with 3 shell attacks.

Super Mario Galaxy 2
A Jellyfish appears in the Cosmic Cove Galaxy.

Trivia

 * In the Prima Official Game Guide for Super Mario Galaxy 2, Jellyfish are called Jammyfish.