In the Hitchhiker's Guide to the Galaxy books, radio plays, TV show and movie, we all know that Zaphod Beeblebrox has two heads:
Mark Wing-Davey as Zaphod Beeblebrox in the TV series
Zaphod's Great Grandfather, Zaphod Beeblebrox the Fourth also has two heads, as indicated in The Restaurant at the End of the Universe:
"Now. Who disturbs me at this time?" said the small, bent, gaunt figure standing by the sprays of fern at the far end of the bridge. His two small wispy-haired heads looked so ancient that it seemed they might hold dim memories of the birth of the galaxies themselves. One lolled in sleep, but the other squinted sharply at them.
However, not all Betelgeusians do. For example, his semi-half-cousin Ford Prefect does not.
I know the film implied his second head was an elective surgical procedure required to run for President of the Galaxy but that wouldn't explain why his Great grandfather did, is there any reason given in the novels why some Betelgeusians have two heads, and some have one?