In 1957, Dave Brubeck and his Quartet recorded an entire album of Disney songs called, fittingly, Dave Digs Disney. I remember first hearing about this from WBGO a couple years ago. I distinctly remember that I was driving home at the time (and even which stretch of road I was on), and thinking "Hmmm..that sounds like an alto sax. That sounds like Paul Desmond's alto sax. That IS Paul Desmond's alto sax!". Then Brubeck's piano came in and I knew I was right. The song was "Heigh-Ho" from Snow White (click here to listen) and I went out and bought the CD the next weekend.
From Dave Digs Disney, here is "Some Day My Prince Will Come":