Originally recorded by Eartha Kitt (US #4 1953).
Other popular versions by Mae West (1966), Eartha Kitt (new arrangement, 1963), Madonna (1987).
From the wiki: “The song is a tongue-in-cheek look at a Christmas list sung by a woman who wants extravagant gifts such as sables, yachts, and decorations from Tiffany’s. It is one of the few hit Christmas songs written by a woman — Joan Javits (the niece of then-Senator Jacob K. Javits), and Philip Springer.
“‘Santa Baby’ was first recorded by Eartha Kitt with Henri René and his orchestra in New York City on October 6, 1953. The song was a huge hit for Kitt, and she later said that it was one of her favorite songs to record.
“Kitt reprised the original song in a 1963 re-recording for Kapp Records, with a more uptempo arrangement. Madonna’s popular rendition, for the 1987 charity album A Very Special Christmas, was based on this latter arrangement.
“Bawdry and flirtatious actress Mae West covered ‘Santa Baby’ in 1966 for her album Wild Christmas. West inserted her own catchphrases into the songs’ lyrics for parody effect.”
Eartha Kitt, “Santa Baby” new arrangement (1963):
Mae West, “Santa Baby” (1966):
Madonna, “Santa Baby” (1987):