Wolfgang Amadeus Mozart
One famous clarinet composer was classic composer, Wolfgang Amadeus Mozart, who composed the best known clarinet classical piece, written in 1791 “The Concerto in A” in which featured the clarinet. Mozart was especially fond of the clarinet, especially the basset horn (in the clarinet family) as it became his favourite instrument from 1780.
Sample of the first movement in "The Concerto in A"
Karl Maria von Weber
The famous German Karl Weber also wrote very popular pieces in which featured clarinets. He very well knew the strengths and the weaknesses of the instrument and is able to incorporate that knowledge very effectively into writing great pieces to be played on the instrument that will highlight its strengths. He wrote these pieces for his good friend and excellent clarinet player, Heinrich Baermann. It have been claimed that he wrote the second most popular pieces for the clarinet after Mozart. His famous piece was "Clarinet Concerto Number 1 in F-minor"