The Anvil of Fury is an anvil in Diablo I and Diablo: Hellfire. In the quest with the same name, Griswold will ask you to retrieve this item for him, so that he may use it to forge Weapons. The anvil can be found on a peninsula on the tenth level of the dungeon (the second level of the Caves), where it is heavily guarded.
In Diablo III, at the remains of the Griswold's Armory; there is a weapons rack, occasionally there is what looks to be a slab of rock with a weapon upon it; when you hover the pointer over the Slab, it registers the name "Anvil of Fury".
When used, the Anvil will spawn a weapon, which has a chance of being the semi-legendary item Griswold's Worn Edge.