Hit TV shows or movies usually was the inspiration to record an album or at least release a single.  Some were good at it, some were---well you can judge for yourself should you ever come across their material.  This list if far from complete, should you have additions, corrections, or even scans of the albums I would appreciate hearing from you.

Barbie Benton (Playboy Playmate and actress) released an album in the 1978 called "Ain't It Just The Way".  I think this was a UK release, although I am not sure.
Terry Bradshaw (Pittsburgh Steeler's player) released several albums, "I'm So Lonesome I Could Cry" and a gospel album "Until You".
Danny Bonaduce (Danny Partridge of the Partridge Family) released an album in 1973. Also released that year were several singles, "I'll Be Your Magician/Fortune Lady", "Dream Land/Blueberry You".
Lynda Carter (Diana Prince better known as Wonder Woman) released an album in 1978 called "Portrait".  I heard rumors of Lynda doing a follow up to this album, does anyone know if it happened?
Ralph Carter (Michael from Good Times) released an album in 1976 titled "Young and In Love".
Ted Cassidy:  Did a novelty song called The Lurch, not sure what year!
Cliff De Young released a single in 1974 called "My Sweet Lady".
Barbara Eden (Jeannie of I Dream Of Jeanie) released an album called "Miss Barbara Eden" in 1967.  Also released in 1967 were several singles, "I Wouldn't Be A Fool/Bend It", "Rebel/Heartaches", "I'm A Fool To Care/Pledge of Love".
Sally Field (Sister Bertrille on The Flying Nun) released an album "Sally Field, Star of the Flying Nun in 1967.  Also released in 67 were several singles "Felicidad/Find Yourself a Rainbow", "Months of the Year/Gonna Build A Mountain", "You're A Grand Old Flag/Golden Days".
Lorne Greene: (Ben Cartright on Bonanza) recorded a single in 1964 that went to number one it was called "Ringo".  Lorne also recorded at least three albums--"Five Card Stud", "Young At Heart" and "The Man".
Lisa Hartman-Black (CiJi on Knots Landing) probably best remembered for her  role on that night time soap, Lisa released her first album in 1976 and then another album in 1979 titled "Hold On" which was re-released in 1982 under a different title (Letterock). In 1987 another album "Till My Heart Stops" was released, but I am not sure if it was in the US or solely a foreign release--anyone know for sure?  Then of course, the world really did hear Lisa in a big way when she sang back up vocals with her husband, country singer, Clint Black on his Greatest Hits album from 1996.
David Hasselhoff (Knight Rider, Bay Watch) David released an album in the states back in 1985 titled "Night Rocker".  He has since released numerous albums in Europe where he is considered a singing sensation with his material selling millions of copies.
Lawrence Hilton-Jacobs (Freddie "Boom Boom" Washington on Welcome Back Kotter)released a self titled album in 1978 and then another in 1979 titled "All The Way, Love".
Don Johnson (Nash Bridges and Sonny Crocket from Miami Vice) released a solo album in 1986 called "Heartbeat" (which was a million seller) and it's follow up in 1989 called "Let It Roll". 
Jack Klugman and Tony Randall recorded an album called "The Odd Couple Sings".
Chris Knight (Peter on the Brady Bunch) released a single in 1973 titled "Over and Over/Good For Each Other".  Also, released in 1973 was duet album with Chris and Maureen (Marcia) McCormick.
Cheryl Ladd (Chris Monroe on Charlie's Angels) released a self titled album in 1978 and then did a follow up in 1979 with one entitled "Dance Forever". (Cheryl had great success with her recording career in Japan.)
Joey Lawrence:  self titled album in 1993
Peggy Lipton (Julie Barnes on the Mod Squad) released an album in 1968 and then several 45's in 1969.
Mike Lookinland (Bobby on The Brady Bunch) released a single in 1973 "Love Doesn't Care Whose In It/Gum Drop".
Gloria Loring (soap actress--Days of Our Lives) released a single called "Friends and Lovers". Gloria also sings the theme to tv show "The Facts of Life".
George Maharis (Buzz Murdock on the classic 60's series Route 66) released an album called "George Maharis Sings". This was the first of seven albums.  Also, Maharis has released material in places like Japan, Chile, Argentina.
Penny Marshall and Cindy Williams (Laverne and Shirley) released an album in 1976 entitled "Laverne and Shirley Sing".
Jerry Mathers: (Beaver on Leave It To Beave) released a single in 1962.
Maureen McCormick (Marcia on The Brady Bunch) released various singles in 1972 and 73. Maureen still sings and has released a CD several years ago. She has an official website that tells all about it.   
Kristie and Jimmy McNichol release a self titled album in 1978.
Donny Most (Ralph of Happy Days) Donny released an album and several singles in 1976 and then another single in 1980.
Leonard Nimoy: Released numerous albums over the year, two of which are "The Way I Feel" and "Two Sides of Leonard Nimoy.
Eve Plumb (Jan on The Brady Bunch) released a single in the 1970's "Fortune Cookie Song/How Will It Be".
Tony Perkins: Recorded an album called "On A Rainy Afternoon".
Burt Reynolds: Recorded and album called "Ask Me What I Am.
Kurt Russell: Self titled album--not sure of the year??
Telly Savalas (Kojack) released, I think, 4 albums, the first in 1973?
John Schneider (Bo Duke on Dukes of Hazzard).  John did have some moderate success as a country singer in the 1980's. 
Ricky Segall (Ricky Stevens on The Partridge Family). In 1973 an album was released called "Ricky Segall and the Segalls" and then in 1974 a single was released "Say Hey Willie/Sooner or Later".
Cybil Shepherd (Maddie Hayes in Moonlighting) released an album in 1968 titled "Cybil Does It To Cole Porter". In 1976 tow more albums one called "Somewhere Down The Road" and the other "Mad About The Boy". In 1978 "Vanilla" and then in 1997 "Talk Memphis To Me".
William Shatner (James T. Kirk on the original Star Trek) released an album called "The Transformed Man".
Elke Sommer (actress) released an album called "Love in Any Language" in 1965.
David Soul (Ken Hutchinson on Starsky and Hutch) beginning in 1977 and then for about 5 years following, David released 4 albums and he had a fairly successful hit with "Don't Give Up on Us, Baby". To be fair to David, he was a successful singer before he became famous as one half of the duo "Starsky and Hutch".  He opened for such acts as Lovin Spoonful, Frank Zappa, The Byrds and more.
Patrick Swayze: Fresh from his success in the film Dirty Dancing", Patrick released a single called "She's Like The Wind"
John Travolta: (Vinnie Barbarino on Welcome Back Kotter) released an album called "Let Her In" and I think there were a few others, anyone know all the details about this, if so email me, please!  :)
Jack Wagner (Frisco Jones on General Hospital) released an 1984 album titled "All I Need" which was a hit single for Jack.  Another album called "Lighting Up The Night" was released in 1985.
Burt Ward:  The Boy Wonder himself
Johnny Whitaker (Johnny Stuart of Sigmund and the Sea Monsters) released an album called "Friends" in 1973 which spawned the single "Friends/You, You" in 1973 also.
Jack Webb (Sgt Friday on classic Dragnet) "You're My Gal".  He talks the words instead of sings, much like William Shatner's "singing" style!
Mae West: Released several albums on which she sings, "Way Out West" is one of them.
Anson Williams (Warren "Potsie" Webber on Happy Days") released a single in 1977 "Deeply/I Want To Believe In This One".
Barry Williams (Greg Brady on the Brady Bunch) released a single in 1973 "Sweet Sweetheart/Sunny".
Bruce Willis (David Addison on Moonlighting) recorded an album called the "Return of Bruno" which spawned a few hit singles.
Tom Wopat (Luke Duke on Dukes of Hazzard)