It is Hugh Laurie, better known as "House" in this 1992 video for Annie Lennox's "Walking on Broken Glass" (John Malkovich is also in the video)

The article in Spinner also listed 9 other other celebrities in music videos before they were famous, including Angelina Jolie in one for the Rolling Stones, Keaunu Reeves in one for Paula Abdul, and Johnny Depp in a Tom Petty one.

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From the Upcoming ueue, submitted by KMOM14.