The most popular are The Mikado , H.M.S. Pinafore and The Pirates of Penzance . Sir Arthur Seymour Sullivan MVO ( 13 May 1842 â `` 22 November 1900 ) was an English composer , of Irish and Italian descent , best known for his operatic collaborations with librettist W. S. Gilbert , including such continually popular works as H.M.S. Pinafore , The Pirates of Penzance , and The Mikado .