Fish are a planned passive mob. In the Halloween update, Notch said he would add fish. However, he had limited time, and was thus only able to add them as an item. While there may be a coding for the fish in the game itself, there is not a model that currently exists in-game.

If a mod was coded with the same coding minecraft would crash because it has to be a valid model, not a modded model.

Fish would normally spawn in water which would make using a Fishing Rod easier, because you could see the fish underwater instead of randomly catching one via the use of a fishing rod. Fish heals up to one point of one's regeneration bar. Cooked Fish provide more healing, restoring about two more points than a raw fish would. To produce a Cooked Fish, a player requires a Furnace. Place the fish in the furnace along with a piece of Coal. Just like many other things you cook, the raw fish will turn into a Cooked Fish, which can then be eaten by the player.