Internet sources vary, but on February 12, 1797, Franz Joseph Haydn’s String Quartet, Op. 76, No. 3 (“Emperor”) was first performed (allegedly).
(Some claim that February 12 was in fact the first performance of Haydn’s Gott erhalte Franz den Kaiser, an anthem composed in honor of the birthday of the last Holy Roman Emperor, Franz II, which is quoted at length by the aforementioned string quartet. Given that February 12 happens to be the Emperor’s birthday, it is likely the case that the anthem, and not the quartet, was in fact first performed on today’s date.)
The tune of the quartet’s second movement, of course, eventually became the German national anthem, here ably performed by the Emerson Quartet:
Incidentally, this same Emerson Quartet CD contains a recording of Mozart’s String Quartet No. 19 in C Major (KV.465) (“Dissonance”), which is really killer (and highly recommended in Peter Gay’s biography of the composer):