"Killer Joe" (The Jazztet)

"Killer Joe" (as performed by The Jazztet) is one of those songs that embodies everything most folks think of when they think of "jazz": a catchy melody, musician virtuosity, and soulful urbanity.  Whenever people hear it, even if they don't know its name or who composed it, there's inevitably that moment of recognition: "Oh yeah!  That song!"
Actually, saxophonist and prolific songwriter Benny Golson—a founding member of The Jazztet with trumpeter Art Farmer, wrote the tune in 1959.  As Golson tells listeners in his comedic monologue at the beginning of the group's 1960 recording of the song on Meet the Jazztet, "Killer Joe" is a musical sketch of a well-dressed hipster who kind of glides through life, using his slick charm to bilk women out of money while also avoiding manual labor.
The tune primarily is built upon a simple ascending/descending pattern, played on trumpet.  By itself, the riff doesn't seem like much.  But when paired with some sexy staccato piano chords, walking upright bass, and swinging drums, it absolutely oozes cool.  (The structure and arrangement seem to embody whatever real-life character inspired the song to begin with: nothing too impressive on his own, but the King of Cool when decked out in his finery.)
The bridges and releases that come between the choruses are what make this a perennial favorite of mine, though.  The lush, inventive chord changes on each bridge are sophisticated little departures from that core riff.  Same thing with each verse: each soloist takes a few bars and noodles around, establishing his own groove before swinging elegantly back into the chorus.  
Golson's compositional approach of taking the listener into uncharted territory and then bringing them back to the familiar is pure genius; because, as everyone knows, the homecoming is the sweetest part of the trip.