Rondo alla Turca/
Piano Sonata No. 11
by Wolfgang Amadeus Mozart
Mozart is perhaps the most famous classical composer- I think the choice is obviously between Mozart and Beehoven for that superlative- if you compare their popularity over time you see Beethoven spiking in the mid 20th century but that in recent decades Mozart has surpassed Beethoven. Mozart preceded Beethoven- if you look at the wikipedia entry that actually exists for "Beethoven and Mozart" it says that Mozart was an influence on Beethoven. Beethoven was also a protege of sorts of Joseph Haydn- but their relationship starts a decade after he wrote this Sonata- his most popular song on Last Fm with over one thousand plays a week.
You can also make a case that Eine Kleine Nachtmusik (1787) is Mozart's biggest hit:
I think Eine Kleine Nachtmusik deserves a separate entry- talk about a hit!
Rondo alla Turca was not a stand-alone work, it was part of a larger symphony he wrote- this part is the opening to the third movement. Biographers have long noted the influence on this and other Mozart compositions by Turkish Janissary bands of the 17th and 18th centuries: