Bhagavata
A Bhagavata in Hinduism is a worshiper; in this case he is also the play's narrator and he gives the audience a synopsis of the characters' lives before the start of the play. He is able to talk to the characters during the play and he also reacts to what is happening, especially when he does not approve of one particular course of action or another. He is often more of an observer than the narrator because he is also surprised and taken aback by much of what happens. His symbolic role in the play is to show the audience how unpredictable life can sometimes be.
Devadatta
One of the play's two main protagonists, Devadatta is a fair and slender man who is smart as a whip. His father is a Brahmin and he is both poet and political observer. He is close friends with Kapila at the start and the end of the play but feels a great deal of jealousy when he sees that there is a mutual attraction between Kapila and Padmini. Ironically, he becomes more jealous after he is married to Padmini and still sees his erstwhile friend as a rival.
When his head is put back on Kapila's body he feels that he has the best of both worlds, because he has combined his wit with Kapila's strength, and he has Padmini. However, eventually he body starts to become what it used to be and he is swiftly returned to his soft, flabby form again, which leaves him feeling dissatisfied and grumpy. He and Kapila kill themselves in solidarity at the end.
Kapila
A muscular, dark man, Kapila is the son of an ironsmith, and he is the brawn to Devaratta's brains. He is a man of courage and he has great daring and a sense of adventure. He is a far better friend than Devadatta gives him credit for; he talks to Padmini on his friend's behalf even though it is clear to him that they are a mismatch. He also cuts off his own head in solidarity with Devadatta when he finds his decapitated body. When Padmini chooses to remain with Devadatta's head on Kapila's body, Kapila goes into the forest and withdraws from society. He gradually regains his former fitness and physique but he realizes that this is a hollow, half-existence. He and Devadatta kill themselves in solidarity at the end.
Padmini
Padmini is a beautiful young woman who is the object of desire of both Devadatta and Kapila. She chooses Devadatta because she is attracted by his intelligence but she comes to realize that her sharp tongue is too much for his sensitive nature. She is also very attracted to the physicality of Kapila.
Although it is a complete accident when she puts the wrong heads back on the wrong bodies, it does seem that Padmini is now able to have her cake and eat it too, because she gets the mind that she adores atop the body she craves. This is only fleeting, though, because when the bodies of the men start to readjust back to the way they used to be, she is quickly dissatisfied with her lot again.
Padmini is left alone twice by the men, as they kill themselves and leave her twice. The second time she kills herself too, having been dissuaded from doing so the first time around by the goddess Kali.
Hayavadana
Oddly, while the eponymous character in the play, Hayavadana does not appear that much and is not the protagonist. He is a man with the head of a horse—or a horse with the body of a man, depending on your perspective, born from a woman who married a horse and bore his son. He wants desperately to be made complete, which he defines as being a full man. At the narrator's suggestion, he asks Kali to bless him with this but we find out that although she acceded to his request to be made whole, she elected to make him all horse rather than all man. He is joyful when his human voice, the last vestige of his humanity, fades away at the end.
Kali
Kali is the Hindu goddess of death and she appears to most of the characters during the play. Devadatta sacrifices his head to her, and she does receive both men in the end but only because Padmini has put the wrong heads on the wrong bodies and intense suffering ensued. Padmini also addresses her when she burns herself on the funeral pyre. Kali makes Hayavadana a "complete" horse but in doing so demonstrates the perception that the Hindu gods don't really pay attention and can create as much havoc as good.
Dolls #1 and #2
The dolls are snarky, mischievous, rude, selfish, and prideful creatures. They narrate what is happening to Devadatta and Padmini through the birth of their son, Padmini's dreams of Kapila, and more.
Actor #1
This actor is the first to be shocked by the horse-man Hayavadana. He is tasked by Bhagavata to take Hayavadana to Kali's temple. He also ends up with the child when he passes through a hunters' village and they give him the boy, saying he no longer belongs there.
Actor #2
This actor is frightened by Hayavadana singing the National Anthem.
Child
The child is the son of Padmini and Devadatta, given to be raised by hunters until he is five, and then Devadatta's father, the Revered Brahmin. He is silent and surly, and only begins to use his voice when he laughs at Hayavadana.