A genetic modification formula, used by the Company, is capable of giving special abilities to people who don't have them naturally. The formula consisted of three parts: two halves of a schematic document placed in the care of Kaito Nakamura and Angela Petrelli, and a catalyst, held within the body of Hiro Nakamura. Mohinder Suresh created a genetic modification formula on his own, but his version lacked the catalyst, resulting in negative side-effects. The physical formula was destroyed by Peter and Flint and the paper containing the written version by Hiro. The catalyst was destroyed when Peter and Sylar killed Arthur Petrelli, its host at the time. A few vials which contained the Formula survived but have been tracked down and destroyed.
Ripped into two pieces by Kaito Nakamura when Hiro Nakamura went back in time to destroy it, Kaito had the idea of having it in two pieces in order to conceal it's power in two separate locations. It stayed hidden this way until Hiro opened Kaito's safe and that half was stolen by Daphne Millbrook who was working for Arthur Petrelli and Pinehearst at the time. Shortly after, Daphne stole the second half of the formula from The Haitian. Having both halves of the formula, Mohinder Suresh, who was also working for Pinehearst, discovered that they needed a Catalyst to complete it. He theorized that this Catalyst would be hidden inside a person. Originally Ishi Nakamura, she passed it on to her son (Hiro) at the same time she healed him in a past timeline - thus returning his memories, stripped from him by Arthur Petrelli. (At the time of Mohinder's discovery it was believed that the Catalyst was hidden inside Claire Bennet though, due to her own actions in the past as well as those of Hiro, this was never historically accurate.)
In a future timeline (seen by Peter Petrelli): The formula was used to give artificial powers to anyone who could afford them. This lead to a battle between the original Evolved Humans who wanted equality among people, and those that could see the danger of giving everyone limitless powers.
Ando Masahashi: Believing it will give him the power he most desires (Space/Time Manipulation). Instead, it gives him the the power to supercharge powers which he was able to use on Daphne Millbrook, enabling her to move fast enough to travel through time.
Peter Petrelli: In an attempt to regain his former power (Empathic Mimicry, stolen by his father) Instead, it gives him Power Duplication - the power to duplicate any power absorbed from another Super Human via physical contact. Peter can only duplicate one power at a time after gaining his new power, any new powers duplicated will take the place of the previous one.
Mohinder Suresh: After his own experiments with artificial power generation, Mohinder deveolped his own serum and tested it on himself. He was given an imperfect artificial power, allowing him to cling to walls in similar fashion to some type of mutated insect or bug. Unfortunately a side-effect to his incomplete formula caused a horrific mutation - covering him with scales and allowing him to spin spider-like webs, which he uses to ensnare several people in his lab (formerly the studio of Isaac Mendez).