Grammy Award records
The record for the most Grammy Awards won in a lifetime is held by Georg Solti, a Hungarian-British conductor who conducted the Chicago Symphony Orchestra for twenty-two years. He has won a total of 31 competitive Grammy Awards out of 74 nominations and was awarded a Grammy Lifetime Achievement Award in 1996.
Grammy Award for Best Song Written for Visual Media
Alan Menken has the most wins (5 times). After him, only James Horner, Howard Ashman and T Bone Burnett have multiple wins (2 each).
Diane Warren has the most nomination with 10, followed by Alan Menken with 9, Babyface with 7, James Horner and T Bone Burnett with 4 each, Madonna, Howard Ashman, Tim Rice and Michael Kamen with 3 each (all of them won at least one Grammy).
Sting is the most nominated artist without wins (nominated 3 times). Stephen Sondheim, Elton John, Elvis Costello and U2 were nominated 2 times without winning. 
Babyface was the artist with more nominations in a single year with 3 nominations in 1997 but failed to win the award that year.