Kennedy has done much to popularise classical music, particularly among young people. He has also performed and recorded most of the major violin concerti.
Though his aggressive personality is seen by some as abrasive and has limited his career, many respected musicians hold him in high esteem. With one of these, 'cellist Lynn Harrell, he has recorded a well-received album of duets.
Kennedy expresses concern for the immediate appeal of live performance, and often records entire works or movements in single 'takes' to preserve this sense in his recordings. He also introduces improvisatory elements in his performances, as in his Jimi Hendrix-inspired cadenza to the Beethoven violin concerto and his jazz and fusion recordings.