The saxophone in its many different forms is an essential instrument in the jazz genre and for almost any funk, blues or contemporary ensemble. In jazz big bands the saxophone sections provide the essential melodic and harmonic structures of almost any arrangement; their ability to harmonize and double up on lines to punch through the mix is one of the defining characteristic of jazz big band music. In smaller combos the saxophone is associated with some of the most famous jazz musicians ever, including John Coltrane, Charlie Parker, Sonny Rollins, Stan Getz, Cannonball Adderley, Wayne Shorter and countless others.
Arguably the least common saxophone in most jazz and contemporary ensembles. The soprano saxophone is also a Bb instrument but is pitched one octave higher than the tenor sax (sounds a 2nd lower than written) and produces a higher pitched and much more piercing tone than the alto, tenor or baritone. Many famous saxophone players know for playing other variations have some compositions on the soprano, notably John Coltrane and Wayne Shorter.
A staple of both big band and smaller jazz the alto saxophone is an Eb transposing instrument (sounds a 6th lower than written) pitched between the soprano and tenor. The alto produces a more piercing tone than the tenor saxophone but not quite as much as the soprano and can be used as both a melodic or harmonic instrument in an ensemble/section.
Common in almost every genre the tenor sax is a Bb transposing instrument pitched one octave lower than the soprano (sounds a 9th lower than written). While the tenor is (arguably) the instrument of choice in rock, blues and funk it is about as common as the alto in the jazz and fusion genres. An incredibly versatile instrument it produces a darker, lower tone than the alto saxophone.
Most common in jazz and funk big bands the baritone saxophone is an Eb transposing instrument (sounds a 13th lower than written) and is pitched one octave below the alto saxophone. Used to fill out the bottom end of the saxophone section.