- Was the original choice to play "Eddie Munster," in the cult 1960s TV series The Munsters (1964). However, his parents did not approve of the makeup young Bill would have to wear for the role; they turned it down. Butch Patrick ended up playing the part. Today, Patrick and Mumy are very good friends and sometimes collaborate on music.
- Wrote a screenplay back in the late 1970s in which the Lost in Space (1965) family would have found their way back to Earth. 20th Century Fox was committed to the project, but series creator Irwin Allen wasn't interested in reviving the series. The plan dissolved completely after the death of space patriarch Guy Williams in 1989.
- Acted in an episode of the revived The Twilight Zone (2002) TV series with his actress-daughter Liliana Mumy. As a child, Mumy appeared in three of Rod Serling's classic The Twilight Zone (1959) episodes (Long Distance Call (1961), It's a Good Life (1961) and In Praise of Pip (1963)).
- Was a lifelong friend of James Stewart, with whom he co-starred in the film Dear Brigitte (1965). The Stewart and Mumy families knew each other well off-screen, Stewart's wife Gloria having been Mumy's Sunday school teacher. He can still do a perfect imitation of Stewart's voice, one that frequently cracked Stewart up during his lifetime. They were all members of the Beverly Hills Presbyterian Church.
- On the Babylon 5 (1993) episode, Eyes (1994), he used his album title, "Zabagabee", as an alien word. Series producer J. Michael Straczynski was reportedly not amused, as he didn't feel it was appropriate to promote outside projects, and it ran counter to his mandate forbidding improvisation on the show.
- Last name is pronounced "Moomy" not "Mummy"
- Along with Cloris Leachman, he is one of only two actors to appear in both The Twilight Zone (1959) and its second television revival, The Twilight Zone (2002).
- Had a recurring role as "Lennier" on Babylon 5 (1993). Ira Behr, producer of Star Trek: Deep Space Nine (1993), offered him role on the show, but at the time, he was tied up on Babylon 5 (1993). After Babylon 5 (1993) wrapped, Ira offered him a role a second time, but it was as an alien, which Mumy was not interested in doing. When he was offered the chance to portray a human during the final season of the series, he accepted the role in the DS9 episode, The Siege of AR-558 (1998) (he was the Starfleet engineer who worked on trying to decode a Dominion communications array).
- Credits his Lost in Space (1965) co-star Guy Williams with inspiring him to become an actor. Mumy grew up watching Williams on Disney's Zorro (1957) TV series; young Bill broke his leg attempting to recreate one of the show's stunts in his bedroom.
- 'Weird Al' Yankovic was a big fan of Lost in Space (1965) growing up, and he and Mumy later became good friends. Mumy reportedly introduced Al to his wife Suzanne.
- When Bill first appeared as Will Robinson in the popular TV series Lost in Space (1965), he was just a child actor. Over 50 years later he became the only actor from the original series to reprise a role in the remake Lost in Space (2018) when he played Real Dr. Smith in the pilot only.
- Was in the band Seduction of the Innocent with his friends Miguel Ferrer and mystery novelist Max Allan Collins. Seduction often performed in and around San Diego Comicon, and Ferrer's good friend Brandon Lee would sometimes roadie for the group.
- Performed with Robert Haimer as "Barnes & Barnes", recording the hit novelty song "Fish Heads" in 1978. It is currently the most requested song in the history of the Dr. Demento Show.
- His acting mentor was "Lost In Space" co-star Jonathan Harris. Mumy and another LIS co-star, Mark Goddard, both served as pallbearers at Harris's funeral.
- Best known by the public for his role as Will Robinson on Lost in Space (1965).
- He had the honor of being the first American actor to kiss Brigitte Bardot on-screen (in Dear Brigitte).
- In an interview with the Television Academy Foundation, Mumy said that his acting coach in the 1960s was Lois Auer. He would typically spend an hour with her to prepare for any television episode or film he appeared in.
- He has played Cloris Leachman's son four times: in My Own Master (1960), It's a Good Life (1961), Keep an Eye on Santa Claus (1962) and It's Still a Good Life (2003).
- He is of German, English, Scottish, and French-Canadian descent.
- Wife Eileen Mumy is a childbirth instructor.
- He is of English, Scottish, French-Canadian, German, and one quarter Polish Jewish, descent.
- Father-in-law of Alexa Cline.
- He earned his first acting role at the young age of 6 on an episode of TV's National Velvet (1960).
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