Her full name was Cherilyn Sarkisian LaPierre before she got married, until it was legally changed to Cher.
She's 5' 8", was diagnosed with dyslexia at age 30, and has been married to Sonny Bono and Greg Allman. She also lived with rock star Gene Simmons of KISS for several years. Her father was Armenian, her mother was part Cherokee. Her daughter is Chastity Bono, and son is Elijah Blue Allman.
She was offered the part of Thelma in Thelma and Louise, and wanted to be Mrs. Addams in The Addams family, but didn't get the part.
She beat out Celine Dion's "My Heart Will Go On" for the best selling single of 1998 with "Believe." Her music video "If I Could Turn Back Time" was banned by MTV. I never saw more than a clip, but it was part of a live concert on an american Battleship (the Missouri?) and she A) wore some kind of G-string, and B) straddled a huge gun/cannon barrel in the video, while all the navy there were cheering.
There have been rumors that she has had ribs removed to make her thinner, and tons of plastic surgery.
Her most famous movie is probably Moonstruck, and she made headlines again after she gave a moving eulogy of Sonny Bono. There's a decent VH1 Behind the Music special of her. She still makes new albums, although she's over 40, and they sorta sound the same.
My favorite tidbit about her? She actually said on TV that she once thought Mount Rushmore was a natural phenomenon. Like wind and erosion actually carved four contiguous statues of famous American Presidents. Also, she thought the moon was the opposite side of the sun. I believe she dropped out of high school.
Her movie filmography (but scores of TV appearances missing) from IMDB:
Mayor of Sunset Strip (2001) .... Herself
Cher: Live in Concert from Las Vegas (1999) (V) .... Herself
Tea with Mussolini (1999) .... Elsa Morganthal Strauss-Armistan
Nine (1996) (VG) (voice) .... Isadora
Faithful (1996) .... Margaret
Flashbacks 2: Pop Parade (1994) (V) (as Sonny and Cher) .... Herself
Prêt-à-Porter (1994) .... Herself
... aka Ready to Wear (1994)
Cher: Extravaganza - Live at the Mirage (1992) (V) .... Herself
Cherfitness: Body Confidence (1992) (V) .... Herself
Grand Opening of Euro Disney, The (1992) (TV) .... Herself
The Player (1992) .... Herself
Mermaids (1990) .... Rachel Flax
Pee-Wee Herman's Christmas Special (1988)
Suspect (1987) .... Kathleen Riley
Moonstruck (1987) .... Loretta Castorini
The Witches of Eastwick (1987) .... Alexandra Medford
Mask (1985) .... Francais 'Rusty' Dennis
Silkwood (1983) .... Dolly Pelliker
Come Back to the Five and Dime, Jimmy Dean, Jimmy Dean (1982) .... Sissy
"The Sonny and Cher Show" (1976) TV Series .... Co-Host
"The Sonny and Cher Comedy Hour" (1971) TV Series .... Herself/Host
Sonny & Cher: Nitty Gritty Hour (1970) (V) .... Herself/Host
Chastity (1969) (as Chér) .... Chastity
Good Times (1967) .... Herself
Wild on the Beach (1965) .... Herself
... aka Beach House Party (1965)
Thanks TheBooBooKitty for corrections