Bing Crosby, I Don't Stand a Ghost of a Chance With You
Charlie Chaplin, Smile
David Raksin, Laura
Sigmund Romberg, Lover Come Back to Me & Softly As In a Morning Sunrise
Franz Lehár, Vilia
Eden Ahbez, Nature Boy
Bronislau Kaper, On Green Dolphin Street & All God's Chillun Got Rhythm
Truman Capote, A Sleepin Bee
(Of course on some of these the contribution was minimal)
Maybe not jazz standards, but It's All in the Game was written by US vice president Charles G. Dawes and You Are My Sunshine by Louisiana governor Jimmie Davis