As a student, when you learn to play jazz, you need to start by listening to the greats.  Here is a list of a few for each instrument (in no specific order, these are not the only ones to listen to, but merely a starting point):  

Flute                                                       

• Hubert Laws                                    

• Yusef Lateef                           

• Herbie Mann                                   

Clarinet

• Sidney Bechet  

• Benny Goodman  

• Eddie Daniels 

• Anat Cohen

Saxophone                                   

• Charlie Parker                                  

• John Coltrane                                  

• Cannonball Adderley                         

• Sonny Rollins                                                       

• Joe Henderson                                              

• Kenny Garrett                          

• Michael Brecker                                                

• Coleman Hawkins                               

• Lester Young                        

• Wayne Shorter                              

• Joshua Redman                         

• Ornette Coleman                              

• Dexter Gordon             

• Sonny Stitt  

• Jackie McLean  

Trumpet                            

• Miles Davis   

• Freddie Hubbard  

• Clifford Brown  

• Lee Morgan   

• Roy Hargrove  

• Wynton Marsalis 

• Louis Armstrong 

• Dizzy Gillespie 

Trombone

• Curtis Fuller  

• Julian Priester   

• J.J. Johnson  

• Steve Turre

• Robin Eubanks 

• Slide Hampton   

• Trombone Shorty

Piano                             

• Bud Powell 

• Chick Corea                      

• Horace Silver                     

• Thelonious Monk 

• Herbie Hancock                 

• Red Garland                      

• Count Basie                      

• Duke Ellington                 

• Ahmad Jamal               

• Bill Evans                         

• Oscar Peterson                

• McCoy Tyner                     

• Art Tatum                         

• Cedar Walton                    

• Brad Mehldau

• Dave Brubeck      

• Jon Batiste              

Guitar 

• Joe Pass 

• Grant Green

• Wes Montgomery 

• Pat Metheny  

• Kenny Burrell 

• Herb Ellis  

• Pat Martino  

Vibes

• Bobby Hutcherson 

• Gary Burton

Violin  

• Regina Carter                                      

Voice

• Ella Fitzgerald  

• Sarah Vaughan 

• Billie Holiday 

• Bessie Smith 

• Ray Charles

• Nina Simone                                          

• Dinah Washington 

• Carmen McRae

• Etta James

• Bobby McFerrin 

• Kurt Elling

• Nat King Cole 

• Louis Armstrong 

Bass

• Ron Carter 

• Jaco Pastorious  

• John Patitucci

• Christian McBride 

• Paul Chambers

• Jimmy Garrison

• Ray Brown 

• Charles Mingus 

Drums

• Elvin Jones 

• Roy Haynes 

• Max Roach  

• Gene Krupa 

• Philly Joe Jones 

• Billy Higgins 

• Jack DeJohnette

• Jeff “Tain” Watts

• Brian Blade 

• Art Blakey 

Twelve bar blues in every key

Make sure to transpose if you are a Bb or Eb instrument!

Concert C

Concert F

Concert Bb

Concert Eb

Concert Ab

Concert Db

Concert Gb

Concert B

Concert E

Concert A

Concert D

Concert G

Here is a short list of great classical composers and a few of their most famous pieces, to check out (from all different eras):

 Bach

• Toccata and Fugue in D minor, Jesu Joy of man's desiring, Fugue in G minor,  The well tempered clavier,  Air on G string

Mozart

• Requiem,  Eine Kleine Nachtmusik,  Jupiter, Clarinet Concerto, The Magic Flute

Beethoven

• Moonlight Sonata, Violin Sonata #9, Fur Elise, Turkish March, Symphony #5 in C minor

Brahms

• Hungarian dance #5, Lullaby, Symphony #3 opus 90, Symphony #1 in C minor, Cello sonata in F major

Debussy

• Claire de lune, Reverie, Deaux arabesques, Golliwog's cakewalk, Doctor gradus

Mussorgsky

• Night on bald mountain, Pictures at an exhibition, A tear, Songs and dances of death

Monteverdi

• Vespers of 1610, Madrigals book 5, Il Combattimento, - Il Ritorno. The coronation of Poppea

Vivaldi

• Four seasons, Gloria, Stabat Mater, Nulla in mundo, Concerto for two trumpets

Handel

• Messiah, Water Music, Israel in Egypt, Largo, 12 concerti grossi

Haydn

• String quartet opus 64, String quartet opus 76, The seven last words of Christ, Nelson mass, The creation

Schubert

• Trout quintet, Unfinished symphony, Death and the maiden, Inpromptus, Great symphony

Strauss

• Also sprach zarathustra, An alpine symphony, Death and transfiguration, Der rosenkavalier, Don Juan

Chopin

• Nocturne 9 in Eb, Funeral March, Prelude in E minor, Polonaise Fantasie, Ballade #1 in G minor

Schumann

• Carnaval, Piano concerto in A minor, Piano quintet in Eb major, Ditchterliebe, Symphony #3 in Eb major

Tchaikovsky

• 1812 Overture, The nutcracker, Swan lake, The sleeping beauty, cPiano concerto #1

Mahler

• Ressurection, Symphony #6, Rucket Lieder, Symphony #9, Das lied von 

Rachmaninoff

• Prelude in C# minor, Piano concerto #2, Sonata for piano and cello, 10 preludes, Symphony #2 in E minor, The isle of the dead