There are a good number of items which are designed for post-ascension content but have been hacked from the database. These include the ring setting, jewelry-making pliers, floral print shirt, voodoo doll, and exactly-three-shaped box. Except for the voodoo doll, these have all become common.
These are items which were created with the intent to be entered into the game, but hacked before they could be, then changed entirely on the whim of Jick. Single-Minty Gum, Double-Minty Gum, Triple-Minty Gum and Quadruple-Minty Gum have turned, collectively, into the four varieties of gum available South of The Border. It is not possible for these to exist at all, because they have been replaced in the database.
Items Never Released
These are items which were coded but never actually entered deliberately into the game. They were brought into existence by arbitrary item-creation bugs and while they are available on the market, they are somewhat risky to deal in as they may be changed or removed at any time (like the minty gums above). The only item remaining in-game that fits this description is the Children's Meal of the Damned. The can of Red Minotaur was quietly implemented on February 2nd, 2006, and now drops South of The Border.
Items That Never Existed
Well, not really. Item number 666 was hacked by BoozerBear even though there was no item with this number. Near the end of the era of meatsinks, Jick created an item with this number, the steaming evil, specifically to be sold by Boozer as a meatsink. There are only 13 of these in the game, and they are considered legitimate, despite being technically hacked into existence. Bananas were intended to be produced from The Curious Monkey, this later turned into the The Traveling Trader.
Items That Cannot Be Made
Sort of; hot stuffing is an item that can only be made by cooking together two items which cannot be cooked using conventional methods. Instead, one must input a url that would be the url if you could actually cook together the items, which you can't, but really you can. In otherwords, yay, hot stuffing!