Monty Norman and John Barry
Can you imagine a Bond film without an earth-shattering title song performed by Shirley Bassey, Tina Turner, or Madonna? You don't have to imagine it. No, this isn't a dig at Sam Smith's comparatively wimpy theme for Spectre. Dr. No is a Bond film without a title theme.
The title theme was almost the jaunty little ditty "Underneath the Mango Tree" written by Monty Norman for Honey to be singing as she emerged from the salty sea. The song was intended not only to be the film's main theme, but also to be played instead of the James Bond theme we all know and love today.
When the producers realized hey, there might one day be a Bond movie without mangoes in it, they approached Monty Norman to write the theme that has played in every Bond movie since. They still got their money's worth from the "Mango" song, playing it in Miss Taro's bungalow and at the bar where Bond first meets Quarrel.
Or did they ask John Barry to do it? (Don't sue us!) Although Monty Norman has collected royalties for writing the theme since 1962, John Barry, who orchestrated the theme, also claims to have written it. Barry says the producers were unhappy with Norman's theme, and that he re-wrote it for only a 250-pound flat fee.
Norman v. Barry has been a rivalry as fraught as Bond v. Blofeld. In 2001, Monty Norman won a libel suit against the Sunday Times for claiming that Barry wrote the theme. (Source)
Neither of these men seem like supervillains of the same caliber as Dr. No, so we imagine the truth lies somewhere in the middle.