This is Waltz Op. No. 19 in A minor, composed by Frederic Chopin.
This piece was used as a theme in the Chopin - Desire for Love movie:
There is even a song based on this waltz performed by Edyta Geppert, named 'Na krakowskim, czy w Nohant'. So, if you are not a big fan of classical music, but have got an impression you have heard this song before (and wondering where), this may be the answer.