Greed is the second oldest of the Homunculi at the time of the story, younger than Envy. He was created by Dante through an attempted human transmutation of one of her former lovers. Greed and Envy became bitter rivals, probably due to their connections to Dante. At some point in Greed's past, he disobeyed and betrayed Dante and the other Homunculi in some matter. For this, Greed was sealed away in the 5th Laboratory by Envy. The seal that imprisoned Greed was maintained by the skull of the man Greed himself was created from; as remains of the original body paralyze a homunculi, this prevented Greed from simply using his great strength to break free.
Eventually, that skull was jarred loose by the explosion caused by Barry the Chopper in his attempt to escape from Al and Scar. The seal was further broken in a fight between Scar and Gluttony. Thus Greed was set free.
Greed, released from Lab 5.
With his newfound freedom, Greed liberated and recruited the beastmen chimeras that were imprisoned with him; they became his allies to aid him during the inevitable confrontation with the other homunculi. He promised the half-human creatures sanctuary and revenge on the State Military for what they had done to them. Zolf J. Kimblee and Shou Tucker were in Greed's inner circle as well; Tucker would have been killed if it were not for his ability to treat the chimeras and seeking the means of soul transmutation that caught Greed's interest, and Kimblee was under a death sentence from the military. Greed and his followers established their headquarters in the Devil's Nest Bar in the Dublith area, close to where Dante lived.
Unlike the Homunculi who serve Dante (except Envy), Greed has little or no interest in the Philosopher's Stone; he is more interested in money, women, and power, hence his name. Furthermore, Greed does not appear to have the sociopathic tendencies that most of the other Homunculi display throughout the series. Nor does he view humans with contempt as foolish beings he should manipulate. This is evidenced by the many human allies Greed developed, and indeed, even formed caring friendships with.
Greed attempted to recruit Wrath as an ally, but failed. He then abducted Al so he could gain more knowledge on soul transmutation. He claimed he wanted to be immortal so that he could enjoy the fruits of his avarice, but it's possible that Greed was seeking a way to rid himself of what he saw as his one weakness (his body) so that he could not be sealed again. It's possible as well that Greed may have been interested in using soul attachment as a way to become human, which appears to be a subconscious urge common to almost all homunculi. One final possibility exists that Greed wished to know the mechanics of soul transmutation so he could kill Dante.
The abduction occurred in front of Dante, who was held at knifepoint by Greed's followers, who probably did not know who she was. Greed continued to operate out of the Devil's Nest until Kimblee betrayed them, handing over the skull previously used to imprison him to the State Military officer Frank Archer. With two of his closest friends (Roa and Dorchette) killed by Lust and Gluttony during his escape, and seeing his chances for freedom slipping away, Greed decided to wager all he had left and confront Dante. It is unclear if Greed intended to fight Dante, or to beg her forgiveness. Dante, however, had made it appear that Lyra had killed her, stunning Greed long enough for Dante (now incarnated in Lyra) to activate a Flamel array to seal Greed away for good. Dante was in possession of Greed's remains besides the skull, which had their characteristic effect on Greed. Greed somehow gathered the strength to escape but he had already vomited out all the incomplete Philosopher's Stones inside his body, further weakening him for the ensuing fight with Edward.
Knowing that the only possible outcome was to be captured and sealed once more, Greed chose instead to die fighting Edward, confiding in him the secret to defeating homunculi. Thusly, Greed deliberately does not tell Ed that he has let Al go, or that he had nothing to do with the "death" of Dante. After a prolonged fight, Ed stabbed him through the heart after transmuting away his shield; Greed had assumed that his shield could not be penetrated. As he lay dying, Greed revealed to Ed the true weaknesses of his Homunculi brethren (that when confronted with remnants of the human they were intended to be, all their power dissipates and they are paralyzed, and vulnerable to sealing) and encourages Ed to defeat the others. Greed dies in a rather peculiar series of flinches, but Ed thinks he is not dead. It then dawns on Ed that the Homunculus is dead, and Ed breaks down in tears, as he has never killed anyone before. The fact that Greed acted so much more human than the other Homunculi made it difficult for Ed to accept his death, but Greed's advice and the lessons he had learned in Dublith would eventually prepare Ed for the battles with Sloth and Envy.
Greed's position in reference to Dante remains unknown. After his escape from the 5th Laboratory, he resided very close to where he knew she lived. He made no attempt on her life, even when his followers attacked inside her house to capture Al. While dying, he said nothing of Dante to Ed and seemed to be only interested in revenge against the Homunculi, yet he continued to refer to Dante as "the bitch" or "hag".