Early in his career, Kraft released his own albums as a piano player. He worked frequently with Bruce Willis, producing his music albums and serving as executive producer on the film Hudson Hawk (which he also contributed story material for and scored). He produced songs for Disney projects like The Little Mermaid and the theme for TaleSpin. He scored the film The Mambo Kings (earning an Oscar nomination for Best Original Song), wrote the theme music for the sitcom Who's the Boss?, and has been executive music producer on several films including Slumdog Millionaire.