I think Trane's Alabama is the best thing I ever heard (thanks for that referral, Ken!).
Heartfelt, deep, intelligent, sophisticated, raw, moves from hauntingly beautiful to wild and intense, brilliant playing, great chords, sweet swinging once it gets going, gorgeous sounds, wonderful arrangement. The free time part at the end is amazing.
Until I heard that it might have been Joni Mitchell's Goodbye Pork Pie Hat
The most all-round pleasing non-serious song I've heard would have to be Bohemian Rhapsody