During the events of Fullmetal Alchemist: Brotherhood, seven deadly homunculi appear, usually to enforce Father's will as his grand scheme unfolds. They are all born of the Philosopher's Stone and embody a deadly vice of the human spirit, which also reflects in their abilities (and sometimes their appearance, too).
As villains, these seven creatures all met their ultimate fate during the course of the story, but if anything, their deaths were even more symbolic than their actions during it. The original manga's author made sure to not waste any of these characters; they all died in fascinating and impactful ways. Let's go over them all and see how they bowed out of the scene.
Lust appears as a vivacious human woman and her weapon is the Ultimate Spear. In her final scene, she tried to dispatch Roy Mustang (the flame alchemist) and Jean, then turned her Ultimate Spear on Lieutenant Riza Hawkeye. But Roy survived Lust's attack by burning his bleeding wounds closed, and he carved a new transmutation circle on his hand. He used his flame alchemy to burn Lust to cinders with repeated blows and Lust marveled at the vision in Roy's eyes. She hoped that one day that vision would be clouded with pain and terror.
Greed died twice. In the first instance, he was dragged back to Father and refused to work for him, so Greed was melted down into Father's Philosopher's Stone. The second time, he was fighting in prince Ling Yao's body as a team. He confronted Father in person during the story's climax. He had learned the true value of friends and wanted to help create a world where his friends didn't have to suffer from the schemes of madmen like Father. So, Greed helped weaken Father at the cost of his own life, crumbling to dust. His spirit gave prince Ling a casual goodbye as it disintegrated.
Envy is an interesting case. He acted arrogant and superior to humans, like the others, but he secretly envied their strength of spirit and power of unity. Humans had faith, friends and hope, and Envy realized that it made them stronger than any homunculus. During the Promised Day, Envy was defeated, and he realized that his attempts to turn the humans against each other was in vain. So, he tore out his Philosopher's Stone and told the humans that he'd give them a chance to prove fairly whether their way of life was right or wrong. He was done looking down on them out of arrogance.
Sloth dug the entire tunnel around Amestris as part of Father's giant transmutation circle and he acted as Father's bodyguard during the Promised Day. This slow homunculus cornered Major-General Olivier Armstrong and her brother Alex Armstrong and gave them a good fight. But he was wearing out, and when Izumi Curtis and her husband Sig showed up, Sloth was soundly defeated, despite his deceptive speed. He tried to persist and take on his enemies once again, but he had taken one blow too many in the battle. With apathetic words on his lips, he crumbled to dust.
Wrath was the human homunculus, born a mortal man, and later infused with a low-power Philosopher's Stone. He gained the Ultimate Eye and could fight with incredible skills while bearing two swords. He fought many heroes during the Promised Day, from Greed to Fuu (one of prince Ling's bodyguards) to Captain Buccaneer to Scar. His duel with Scar was his last and he got his arms torn off. He lay dying, unable to regenerate, and commented on his lack of regrets in life. He was happy that he had chosen Mrs. Bradley to be his wife -- his life was one of anger and malice, but he died quietly.
Gluttony was more of a tool than a fighter during the story, and it was his job to contain a false portal of Truth that Father had created. He also had a keen nose and a sensitive tongue, making him a useful tracker for Lust and the others. However, when he and Pride (the firstborn homunculus) fought Edward, Lan Fan and the others in a dark forest, Gluttony struggled -- and Pride grew impatient. So, Pride turned on Gluttony and ate him, gaining his brother's sense of smell (and appetite) in the process. With Pride powered up, Gluttony became nothing more than a snack.
This is the one, loose exception to the rule. Pride was certainly defeated but he wasn't destroyed for good like the other six homunculi were. A homunculus can regenerate its body if it sustains fatal injuries, and if its Philosopher's Stone runs out of power (souls), Father can re-absorb it and restock it, as he did for Gluttony. It should also be noted that some homunculi have a tiny true form that may appear if their main body is destroyed, such as Envy and Pride. Pride's shadowy body was destroyed when Edward converted himself into a human Philosopher's Stone and confronted Pride's soul -- destroying it with a punch. Pride wasn't completely killed; his body was lost and his Philosopher's Stone was weakened, reducing him to a tiny newborn that could fit on Edward's palm. Ed remarked on how the arrogant Pride had become such a tiny and helpless thing, but he didn't destroy it.
In a somewhat ambiguous epilogue scene, Pride is seen reborn as Selim Bradley with the same human body but younger than he was in the main story. He appears to be about three-years-old and doesn't seem to retain his previous memory or personality. Instead, his forehead has the same circular mark that his true form had, making it clear that Pride was not truly dead. But he was no longer a menace, at least.