Anime - This is the end result of a failed Human Transmutation. Homunculus are created when people bring together the elements required for a human body but lack one thing: a soul. Only a strong will can bind a soul. Edward Elric is the only person shown to be able to do this without the Philosopher Stone. Even Shou Tucker with the stone was unable to bind his daughters soul to his chimera doll.
Manga - In the Manga, the incomplete red stone is injected into it's subject. One of two things will happen: Either the sin incarnate in the red stone will take over the person, and that person will become a Homunculus, or the incomplete stone will kill the person. Think carefully before asking to play a Homunculus. You may lose your character.
"That Person" always named every homunculus that was born for one of the seven deadly sins... saying it was "because you were born of human sin". - Envy in Episode 52: Fullmetal Alchemist Special.
Envy - [Anime] The first Homunculus greated by Hikari no Hohenheim. This Homunculus is gifted with the Ability to change its form into any person that it has seen at least once. Envy's Oroborous is located on his left thigh.
[Manga]
Lust - [Anime] This Homunculus is gifted with the Ability to lengthen her nails into piercing claws and is named "The Ultimate Lance". Lust's Oroborous is located on the center of her sternum over her heart.
[Manga]
Greed - [Anime] This Homunculus is gifted with the Ability to draw forth the carbon in his body to create a black carbon shield completely covering his body. This is harder than even diamonds. Greed's Oroborous is located on the back of his left hand.
[Manga]
Pride - [Anime] This Homunculus is gifted with the Ability to see the outcomes of many different situations, airflow, currents, and other things normally invisible to the human eye. He is also called "The Ultimate Eye". Pride's Oroborous is located on his left eye instead of having an iris and pupil.
[Manga] - Selim Bradley.
[Game - Bluebirds Illusion] In the Fan-Made game "Bluebirds Illusion", one of the endings is where Edward Elric becomes the Homunculus Pride. Pride's Oroborus is located on his left shoulder in the game. He also has various array markings all over his body. [See Photo]
Wrath - [Anime] This Homunculus is gifted with the Ability to use Alchemy. This is due to the body of the Homunculus being offered back to the Gate where he grew up and can trade its limbs for Alchemist's limbs when they summon the Gate. Once the Homunculus escapes the Gate it is NOT yet evil, but once it consumes the red stone it will become evil. Wrath's Oroborous is on the bottom of his left foot.
[Manga]
Sloth - This Homunculus is gifted with the Ability to shift into water. Sloth's Oroborous is located above her left breast.
[Manga]
Gluttony - This Homunculus is gifted with the Ability to consume literally anything. Gluttony's Oroborous is located on his tongue.
[Manga]