The tale of Tantalus is about as old as they come. Even to the folks we call the ancient Greeks, this story is super ancient. He's most famous for his eternal punishment: being trapped forever in Tartarus with fruit and water are forever just out of his reach. One of the earliest mentions of this awful torture pops up in Homer's Odyssey, when Odysseus pays his visit to the Underworld. There are several versions of Tantalus's story, detailing different accounts of the crime that earned him his sentence. In all the versions, however, Tantalus in some way betrays the trust of his father, Zeus, and he's held up as an example to other mortals of what happens when you mess with the gods.
The most horrific version of Tantalus's crime is told by Hyginus in his Fabulae, where we're told that Tantlus cooked his son, Pelops, and tried to secretly feed him to the gods. (Like, dang.) Some scholars believe that the tale of Tantalus is inspired by the fact that ritual human sacrifice was once part of super ancient Greek culture. The fact that the gods are horrified by Tantalus's offering, could reflect the fact that the Greek religion had evolved beyond the need for such horrific sacrifices.
Tantalus might be glad of the fact that there aren't any extant plays around about his downfall and punishment. (It'd have to be embarrassing to have that played over and over again for audiences' entertainment.) Tantalus's ghost does, however, make an appearance in Thyestes, by the Roman playwright, Seneca. In this play, the T-man is forced to urge his grandsons, Atreus and Thyestes, to do some pretty horrific things to one another. The ghost of Tantalus also puts in an appearance in Caryl Churchill's modern adaptation of the play.
The specter of Tantalus doesn't make a direct appearance in the many plays about his famous descendants Agamemnon, Menelaus, Orestes, Iphigenia, and Electra, the most famous of these probably being Aeschylus's Oresteia trilogy, Sophocles's Electra, and Euripides's Iphigenia at Aulis. All the tragic things that happen to Tantalus's descendants though are sometimes blamed on the curse placed on the family by his original crime. So, in a way, the specter of Tantalus hangs above them all. These days Tantalus lives on mostly through the word "tantalize," which is inspired by his famous punishment.