Frédéric Chopin
The great Polish composer Chopin is well known as one of the greatest composers in history. Innovative in both the style and emotional quality of his pieces, Chopin was well known for including elements of traditional Polish music in his work, such as in Polonaise in A flat major, called "Heroic" (Op. 53). Something that I like about Chopin the dreamy quality of many of his compositions, such as Fantasie Impromptu (Op. 66). Though perhaps not as recognizable to the public as Beethoven, Chopin's music is just as enduring.
 
Fantasie Impromptu, Opus 66
One of Chopin's better known pieces, this performance is by the Polish-American pianist Arthur Rubenstein.
 
"Heroic", Polonaise in A flat major, Opus 53
This performance is by my vote for the greatest pianist of the 20th century, Vladimir Horowitz. This isn't his best performance of the piece, but it is good.
 
Scherzo No 3, Opus 39
My favorite Chopin piece, the best performance of this piece is by Martha Argerich, but I couldn't find a decent video of it. This is Yundi Li.