The original Super Mario Bros. introduces two kinds of water-based enemies, the Bloober or Blooper and the Cheep Cheep.
The latter is a pretty generic-looking fish, and in addition to appearing in the underwater stages, there are levels where you have to cross a bridge while Cheep Cheeps are jumping up at you.
Flying fish are a double threat. The Japanese name for this creature is “Pukupuku,” which has something to do with bubbles. I’m not sure why this was Anglicized to “Cheep Cheep”; as this page says, that seems more appropriate for a bird than a fish. Then again, there was a Nintendo Adventure Book that had Cheep Cheeps nesting in a tree.
The Super Mario Bros. Super Show never used Cheep Cheeps, at least not under that name. Instead, they frequently showed Trouters, the fish enemy from SMB2.
In the game, all Trouters do is jump up and fall back down. There are occasions when you have to jump on their heads to cross a waterfall, not a method recommended by the guidebooks. In the cartoon, Trouters are ravenous, with a repeated joke involving one putting on a bib and grabbing a knife and fork when potential prey is near.
Cheep Cheeps do appear in most of the Mario games after SMB2, and come in several different varieties, including giant and spiky types.
Picture by Till Oilenspiegel
SMB3 has two giant varieties, Boss Bass and Big Bertha. These two have the same name in Japanese, and I’ve occasionally seen them mixed up. Super Mario World introduces the Rip Van Fish, which sleeps until someone gets close.
In Paper Mario, one of Mario’s partners is a Cheep Cheep named Sushie, who babysits the young Yoshis on Lavalava Island.
Picture by TanjatheBat
Her daughter’s name is Sashimie. The sequel brings in Chef Shmi, who serves as a cook on a train. Apparently these Cheep Cheeps are able to function outside water for significant periods of time. The fish even managed to swim their way into the Zelda series.
If I didn’t know better, I’d say there was something fishy going on with these guys.