The cover for the Smiths' 1984 eponymous debut (and every subsequent of their LP and single sleeve designs) did not include an image of the band, but instead a film or pop star. The Smiths featured a still of Joe Dallesandro from the Andy Warhol produced, Paul Morrissey directed film Flesh, about a newlywed who prostitutes himself in order to pay for his wife's new girlfriend's abortion. The film also features Candy Darling, whose image was used for the Smith's 1987 single Sheila Take a Bow.
The cover design is credited to Morrissey. Other cover stars (typically reproduced in duotone) include Terence Stamp, Truman Capote, James Dean, Diana Dors and Elvis Presley. Some (Shelagh Delaney, Viv Nicholson) appeared on more than one cover.
Joe Dallesandro is also rumoured to be crotch that Warhol featured on his cover design for the Rolling Stones' Sticky Fingers LP, with its infamous zipper cover (see below post). My conflation of the two can be seen here.