Deep Cheep

Deep Cheeps (originally parsed Deep-Cheeps ) are a special variety of Cheep Cheeps that are first found in New Super Mario Bros. While regular Cheep Cheeps swim straight forward, Deep Cheeps swim toward Mario or Luigi. Deep Cheeps give up pursuing Mario or Luigi if the he swims behind and past them.

New Super Mario Bros.
In New Super Mario Bros., Deep-Cheeps and their larger variants, the Mega Deep-Cheeps, only appear in World 6-5. They chase Mario or Luigi until he passes them.

New Super Mario Bros. Wii
In New Super Mario Bros. Wii, Deep Cheeps are slightly more common. One appears in World 1-4 along with a Mega Deep-Cheep. If Mario and co. keep staying in the area, another pair of green fish enemies appears. Deep Cheeps can also be encountered in the second part of World 8-4.

In this game, their lips have become pink, matching the current depiction of a Cheep Cheep's, rather than keeping the red-orange colored lips they and Cheep Cheeps previously had in New Super Mario Bros. Their dorsal fins and tails have also become yellow, as opposed to white. There is a more relentless enemy similar to Deep Cheep known as Spiny Cheep Cheep.

New Super Mario Bros. 2
Deep Cheeps reappear in New Super Mario Bros. 2, behaving and looking like they did in New Super Mario Bros. Wii. Deep Cheeps first appear in.

New Super Luigi U
Though Deep Cheeps do not appear in New Super Mario Bros. U (despite them receiving official artwork for that game), they still appear in New Super Luigi U, behaving the same as in previous games. Their only appearance is in Cheep Chomp Chase.

Super Mario Maker / Super Mario Maker for Nintendo 3DS / Super Mario Maker 2
Deep Cheeps reappear in Super Mario Maker, Super Mario Maker for Nintendo 3DS, and Super Mario Maker 2. They aesthetically replace green Cheep Cheeps and Blurps in the New Super Mario Bros. U style, except that they no longer chase the player due to the green Cheep Cheeps and the Blurps from other styles not being able to chase Mario. Furthermore, they are referred to in the games simply as Cheep Cheeps.

Mario Party 9
In Mario Party 9, a Deep-Cheep can be seen swimming around Blooper Beach. It jumps out of the water at various intervals and may even jump over the player's vehicle. It has no effect on the gameplay.

Minecraft
In the Super Mario Mash-up in Minecraft, normal Cod fish are reskinned to be Deep Cheeps.

Dr. Mario World
In Dr. Mario World, Deep Cheeps appear in the background of World 18 once an area has been cleared.

Similar enemies
Years before Deep Cheeps debuted, green Cheep Cheeps had existed in the Mario franchise in several games. The Paper Mario series has also featured green Cheep Cheeps that are not Deep Cheeps.
 * In Super Mario Bros. 3, green Cheep Cheeps simply swim back-and-forth in shallow bodies of water, and as such are less aggressive than the red ones of the same game, unlike Deep Cheeps.
 * In the Super Mario All-Stars versions of Super Mario Bros. and Super Mario Bros.: The Lost Levels, green Cheep Cheeps replace gray Cheep Cheeps; the "orange and gray" palette in the originals actually occupies the same hardware space as the "orange and green" palette, as demonstrated by World 9 of the latter.
 * Mr. Kipper from Super Mario RPG: Legend of the Seven Stars, a stronger variety of Cheep Cheep (referred to as "Goby" in this game), is shown to be green out of water, but appears purple while underwater, like the Cheep Cheeps of that game.
 * In Yoshi's New Island, green Cheep Cheeps appear which have the filename for a Deep Cheep. They do not chase after players; instead they swim straight in a wavy pattern.
 * In Super Paper Mario, green Cheep Cheeps, found in The Tile Pool and the Gap of Crag, behave just like their red counterparts, found in Gloam Valley, but always appear fully-submerged, while the red ones are typically right under the surface. They both have the same stats, and the green ones are the one present on the Cheep Cheep Catch Card.
 * Green Cheep Cheeps were going to appear in Paper Mario: Color Splash, as they have graphics in the data, but they are unused in the final version. Deep Cheeps were also unused in Paper Mario: Sticker Star.

Trivia

 * The Green Cheep Charger from Mario Kart Tour resembles a Deep Cheep.