Have The Rolling Stones ever won a Grammy?

If yes, for which record and in which year?

They got an award for Lifetime Achievement in 1989, I believe, and Voodoo Lounge (yes, Voodoo Lounge) won Best Rock Album in 1995.

The lifetime achievement was in 1986 - they got the award the same week as they played the Stu tribute gig at the 100 club and collected their award from Eric Clapton, and it was broadcast on satellite.

Presume youre thinking about the RnRHOF induction in 1989.

The Grammys didnt have a rock category between about 1967 and 1979, which may explain why the Stones (and other greats from that era) have won so few.

Some Girls was nominated for Album of the Year in 1979, their only nomination for the album.

They got a lifetime achievement award in 1986

Harlem Shuffle nominated for Best Rock Vocal Performance by a Duo or Group in 1987

Mixed Emotions nominated for Best Rock Vocal Performance by a Duo or Group in 1990

Almost Hear You Sigh nominated for Best Rock Vocal Performance by a Duo or Group in 1991

Voodoo Lounge won for best rock album in 1995 (well deserved IMO)
Love Is Strong won for best video too (another well deserved award)

Brigdes To Babylon nominated for best rock album in 1998, Anybody Seen My Baby for Best Pop Performance by a Duo or Group with Vocal.

A Bigger Bang nominated for best rock album in 2006

Well if Magic isn't up for best album of the year then it just show's how f'ed up the Grammy's really are.

"It's just some friends of mine and they're busting down the door"

Was Don Was of Was (Not Was) ever nominated ?

In 1995, Don Was earned a Grammy Award for Producer of the Year. In 1997, he directed and produced a documentary, "I Just Wasn't Made For These Times", about former-Beach Boy Brian Wilson. The film debuted at The Sundance Film Festival and won the San Francisco Film Festival's Golden Gate Award. Was received the British Academy Award (BAFTA) for Best Original Score in recognition of his compositions for the film "Backbeat".