It became the third best-selling single of 1990, the 82nd best-selling single of the 1990s, and was certified platinum by the Recording Industry Association of America in April 1990. The song's popularity sent I Do Not Want What I Haven't Got to the top of the Billboard 200 where it stayed for six consecutive weeks.
The clip consists mostly of a closeup on Sinead O'Connor's face and her different stages of sadness as she sings the lyrics; the rest consists of her walking through an area of Paris, known as the Parc de Saint-Cloud. Toward the end of the video, two tears roll down her face, one on each cheek. In the middle and at the very end of the video there is a shot from O'Connor's photo session for the I Do Not Want What I Haven't Got album cover.
In 2004, Rolling Stone placed the Sinéad O'Connor single at number 162 on their list of the 500 Greatest Songs of All Time, which contains only two songs of the 1990s ranked higher.