Today, production of Adamantium is largely under the control of the United States government. Despite many security breaches, the formula is still officially a state secret. The United States apparently licenses different private contractors to distribute Adamantium for them to select clients or projects. Stark International and Hank Pym's private laboratory both had storages of the two main Adamantium resins in Avengers (1st series) #201-202. Adametco was the country's leading manufacturer of Adamantium at one time.
Despite the precautions, many outside agencies have access to Adamantium. AIM possessed the Adamantium resin batches in Avengers (3rd series) #13, indicating they are equipped to forge True Adamantium. Ultron seems capable of creating his own Adamantium bodies these days. The various renegade government programs connected to Weapon X also have the formula, and through them both RoXXon and the Facility gained access as well. Security leaks apparently provided both the Japanese and Soviet governments with information on the Adamantium formula decades ago.
Apocalypse also had access to Adamantium and the bonding process. Indeed, Chris Claremont originally intended Apocalypse to be responsible for Wolverine's skeleton. The primal rage Wolverine experienced in the presence of Apocalypse's handiwork in Uncanny X-Men (1st series) #242 and Wolverine: The Jungle Adventure was meant to be a reference to that. The latter story also had an inexplicable ancient skull forged of Adamantium found in one of Apocalypse's labs. Barry Windsor Smith deliberately created a power behind the Professor in his original Weapon X story so that Claremont could one day tell that origin. At this point, though, it's more likely the voice the Professor was conversing with during the bonding procedure was that of Romulus.