When Mozart first encountered the tone of the basset horn, it became one of his favorite instruments. He incorporated it into almost all of his compositions and even wrote specific music for it.

Maurerische Trauermusik K. 477, Gran Partita K. 361, Requiem K. 626, and several of his operas, such as Die Entführung aus dem Serail, La Clemenza di Tito which features Vitellia's great aria "Non più di fiori" with basset-horn obbligato K. 621, and Die Zauberflöte, where they prominently accompany the March of the Priests, as well as chamber works. He wrote dozens of pieces for basset horn ensembles.

Furthermore, an earlier version of Mozart's Clarinet Concerto, part of the first movement KV 621b in the Köchel catalogue, was scored for basset horn in the key of G.

Beyond Mozart's celebrated work, other composers including Beethoven wrote for it. Moreover, Richard Strauss played a pivotal role in reviving interest in the instrument and reintroducing it to orchestral settings towards the end of the 19th century and into the 20th century. 

You can check out the sound sample video below.