One of the small things I really enjoyed in Diablo 2 was the Horadric Cube. I know Diablo 3 has crafting NPCs, but a list of recipes just doesn't feel as "free" or experimental as jamming some stuff into the Cube and seeing what pops out.
Does the Horadric Cube make a comeback in Diablo 3? Or is it replaced entirely by crafting NPCs?
No, there's no Horadric Cube in D3.
As you already said, your NPCs already have all your bases covered regarding crafting.
Even if this does indeed subtract the "fun" of experimenting, the developers decided to put a more streamlined experience in the game, perhaps trying to appeal a wider audience.
They are implementing an item that is similar called Kanai's Cube and it is now part of the lore that this cube created the Horadric Cube
Crafting in D3 is always an experiment. You'll never know what you'll get. Hence my two handed axe with 120 intelligence, used by my wizard. But, like Kappei said, no cube in D3.
To provide an update and a more thorough answer; Blizzard recently announced the addition of Kanai's Cube, which has been available on the Player Test Realm this month. It is set for release to the main game in August 2015.
If you are familiar with the Horadric Cube in Diablo 2, Kanai's Cube will feel similar but performs radically different functions.
In Diablo 2, the Horadric cube was used primarily to:
Many of those applications have been supplanted by the gem combiner and enchantress in Diablo 3. Kanai's Cube instead will probably have recipes for (based on the PTR realm's experience):
