Java Edition removed recipes

Chainmail armor
Between the introduction of chainmail armor in Indev, and snapshot 14w25a for 1.8, chainmail armor was craftable using fire. As of that snapshot, fire can no longer exist as an inventory item, even with inventory editing, and the recipe itself was removed from the game's registry of recipes.

Chainmail armor may still be obtained in other ways.

Enchanted golden apple crafting recipe
Since their introduction in 1.3.1, and until snapshot 15w44a for 1.9, enchanted golden apples had the following crafting recipe:

Enchanted golden apples may still be obtained in other ways.

Horse armor
In snapshot 13w16a of 1.6.1, a crafting recipe for iron, golden and diamond horse armor was added. In snapshot 13w18a, the crafting recipe was removed; aside from wanting to add more "treasure" items in chests, the reason is still unknown.

Iron, golden and diamond horse armor may still be obtained in other ways.