Schuck was born in Boston, Massachusetts, the son of Mary (née Hamilton) and Conrad John Schuck, Sr., a professor at SUNY Buffalo, of English and German descent.
He made his first theatrical appearances at Denison University, and after graduating continued his career at the Cleveland Play House, Baltimore's Center Stage, and finally the American Conservatory Theater, where he was discovered by Robert Altman. Schuck's first appearance in film was the role of Capt. Walter Kosciusko "Painless Pole" Waldowski in Altman's film M*A*S*H (1970). As Painless, Schuck holds a place in Hollywood history as the first person to utter the word “fuck[ing]” in a major studio film. He went on to appear in several more Altman films: Brewster McCloud (1970), McCabe & Mrs. Miller (1971), and Thieves Like Us (1974).
In 1970 he appeared as Frank Carelli in Episode 5 of the first series of The Mary Tyler Moore Show, "Keep Your Guard Up."
From 1971 to 1977, Schuck appeared as San Francisco Police Detective Sergeant Charles Enright in the television series McMillan & Wife and also starred as an overseer in the miniseries Roots. In 1976, he played Gregory "Yo-Yo" Yoyonovich in the short-lived series Holmes & Yo-Yo; both it and McMillan & Wife had been created, and were produced, by Leonard B. Stern for what is now NBCUniversal Television. He starred in ABC's 1979 TV holiday special The Halloween That Almost Wasn't, a.k.a. The Night Dracula Saved the World, as the Frankenstein Monster. (He would again use the Universal International Frankenstein-monster makeup format in The Munsters Today; see below.) In 1979 John starred in a short-lived TV series version of Turnabout, in which he acted out the role of the husband, Sam, who became the wife, Penny, after swapping bodies with his wife Penny (Sharon Gless) who became Sam. Some installments from that comedy series were reedited into the made-for-TV film Magic Statue, titled after the artifact which caused the two to exchange bodies.
He was also a regular "guest celebrity" on game shows in the 1970s and 1980s, appearing as a guest on such programs as Pyramid, Hollywood Squares, Password Plus and Super Password, and The Cross-Wits.
In the summer of 1979, during this period as a game-show guest celebrity, he made his Broadway debut playing Oliver "Daddy" Warbucks as a replacement in the role of the original Broadway musical comedy, Annie at the Alvin Theatre, for a special three-week engagement. In 1980, Schuck began appearing as a "regular replacement" for a year and a half, along with Allison Smith as Annie and Alice Ghostley as Miss Hannigan.
In 1986, Schuck took the role of Klingon ambassador Kamarag in Star Trek IV: The Voyage Home. He reprised the role in 1991 in Star Trek VI: The Undiscovered Country, becoming one of only five guest roles to appear in more than one Star Trek motion picture. (The others were the characters of David Marcus, Saavik, Sarek, and Fleet Admiral Cartwright.)
Also in the 1980s, Schuck starred as Herman Munster in the syndicated situation comedy The Munsters Today, which co-starred Lee Meriwether as Lily Munster. In character as Herman, a role Fred Gwynne had originated in the 1960s, Schuck was made up as the Frankenstein Monster, according to the makeup format whose copyright NBCUniversal still owns, for the second time in his career; the first (see above) was in The Halloween That Almost Wasn't a.k.a. The Night Dracula Saved the World.
He guest starred in Star Trek: Deep Space Nine as Legate Parn, Star Trek: Voyager as Chorus #3, Star Trek: Enterprise as Antaak, and Babylon 5 as Draal in "The Long, Twilight Struggle" (1995). In 1994, he appeared as Ralgha nar Hhallas (callsign Hobbes) in Wing Commander III: Heart of the Tiger. He then guest-starred in several episodes of Law & Order: Special Victims Unit as the NYPD Chief of Detectives Muldrew.
Under his full name of "Conrad John Schuck," he opened in the role of Daddy Warbucks in the Broadway revival of Annie in December 2006, and toured nationally in the role. He later appeared in the films Holy Matrimony and String of the Kite. In 2013, he appeared as Senator Max Evergreen in Nice Work If You Can Get It.
Most recently, Schuck joined the cast of writer/director Christopher Blake Johnson's indie horror film, All Light Will End, alongside Andy Buckley and Sam Jones III.
Schuck married actress Susan Bay, and together they had a son named Aaron. The couple divorced in 1983.MASH (1970) - Capt. 'Painless' Waldowski
The Moonshine War (1970) - E.J. Royce
Brewster McCloud (1970) - Officer Johnson
McCabe & Mrs. Miller (1971) - Smalley
Hammersmith Is Out (1972) - Henry Joe
Blade (1973) - Reardon
Thieves Like Us (1974) - Chicamaw
Midway (1976) - Wilson (uncredited)
Butch and Sundance: The Early Days (1979) - Kid Curry / Harvey Logan
Just You and Me, Kid (1979) - Stan
Earthbound (1981) - Sheriff De Rita
Finders Keepers (1984) - Police Chief Norris
Star Trek IV: The Voyage Home (1986) - Klingon Ambassador
Outrageous Fortune (1987) - Atkins
The New Adventures of Pippi Longstocking (1988) - Capt. Efraim Longstocking
My Mom's a Werewolf (1989) - Howard Shaber
Second Sight (1989) - Manoogian
Dick Tracy (1990) - Reporter
Star Trek VI: The Undiscovered Country (1991) - Klingon Ambassador
Holy Matrimony (1994) - Markowski
Pontiac Moon (1994) - Officer
Demon Knight (1995) - Sheriff Tupper
The Curse of the Jade Scorpion (2001) - Mize
Closer to God (2014) - Sydney