Malachi Constant
The protagonist of the novel, Malachi Constant is an American multi-billionaire with an inordinate abundance of good luck. He is shallow and hedonistic, but when his life takes a quick downturn, he begins a long journey around the galaxy, exactly in keeping with the predictions of Winston Niles Rumfoord. It's interesting to note that Constant doesn't seem to be able to exert his will to any significant effect in this novel; he seems to be merely a passive spectator in his own life, which is a common theme for Vonnegut's characters.
Winston Niles Rumfoord
Rumfoord is a wealthy, authoritative man with an air of incredible charisma and solidity, despite the fact that he now exists as a sort of waveform, spiraling between the Sun and the star Betelgeuse, only appearing on planets for short periods at regular intervals as these planets align with Rumfoord's planes of existence. He can also see the past and the future with equal ease, and his predictions and interventions are the primary driving force behind the events that make up the plot.
Beatrice Rumfoord
Beatrice is the wife of Winston Niles Rumfoord, and they have had a falling out after he told her that she would be bred with Constant on Mars to produce a son. She is a strong, independent woman, and she holds on to her values with patience and determination (and often quite a bit of stubbornness).
Salo
Salo is the Tralfamadorian alien stranded on Titan. He had been sent as a messenger from Tralfamadore, but his ship broke down, and he's been waiting for a replacement part for millennia. It is revealed that Salo's malfunction is the primary cause of the development of human civilization, as the Tralfamadorians have been controlling them in order to make them manufacture the part Salo needs. He's a small, self-destructive little robot, and his feebleness makes the point seem even more inane.
Chrono
Chrono is the son of Malachi Constant and Beatrice Rumfoord, conceived on Mars when Constant was "Unk" in the Martian Army. Chrono is an independent boy, and he rejects his father when they first meet. This independence is obvious throughout the book, but he inadvertently acts as the savior of Salo by transporting a piece of metal he calls his "good luck piece," which has far more implications than even Chrono himself thinks.
Boaz
Boaz is one of the commanders of the Martian army, living undercover as just another soldier. He befriends Unk, whom he knows to have been a successful Earthling, so that when the invasion begins, they can defect and simply have a good time on Earth. Boaz also ends up becoming stranded on Mercury with Constant, and they actually develop a friendship once Boaz gets past his hedonistic ways.
