Milan Kundera in The Unbearable Lightness of Being frequently references both the Czech identity (at least implicitly and indirectly) and music. I don't think that it is coincidental that a great deal of the most well-known Western classical music has come out of the modern Czech republic. During the 19th century the territories of the Austrian empire then known as Bohemia and Moravia served as the homeland of several of the most important pioneers of nationalist music, like Smetana, Dvořák, and Janáček. Before those composers, music had primarily been focused either on the church (in the 18th century and earlier) or on satisfying particular patrons. The Czech composer Bedřich Smetana, building on the earlier examples of Chopin and Verdi, wrote some of the first entirely nationalist music, built around folk melodies and programs from folklore or the natural landscapes of Bohemia.
While Smetana pioneered the Czech style, in terms of international recognition Antonín Dvořák is by far the most famous Czech composer, and in his technical style he was probably the most innovative. Dvořák was born in 1841 near Prague. He was trained as a musician, and played as a violist in an orchestra as well as an organist. He increasingly composed symphonic works on the side, and by 1878 his string quartets had won him a good deal of fame. Nationalist pieces like the symphonic version of his piano duet Slavonic Dances further gained him the attention and support of composers like Brahms. In 1892 he began a stint in New York that lasted 4 years; during this period he composed his 9th Symphony From the New World, which is his most famous piece and among the most-performed symphonies of any composer (it's a bit ironic that a nationalistic Czech composer is most well-known for his imitation of American music) and his American string quartet. Upon his return to Bohemia he composed five somewhat sentimental symphonic poems based on his life and Czech folklore, which are my favorite Dvořák compositions. Here is a recording of one of them, The Water Goblin (1896) by the Janáček Philharmonic Orchestra:
The symphonic poem is based on a Czech poem, which is in turn supposedly based on folklore. It is highly programmatic and tells the story of a woman and her daughter, who live by a lake inhabited by a water goblin. The daughter, against her mother's advice, walks over to the lake, falls in, and is abducted by the goblin. The goblin forces her to marry him and they have a child. The daughter convinces the goblin to allow her to her return to her mother for a single night, but she does not return to the goblin by morning, and after a storm the mother and daughter find the baby's decapitated body outside their door.
The initial theme played by the flutes is the water goblin's motif; the emphasis on the first three beats of every four-beat measure continues virtually throughout the piece. At about 1:47, the daughter's theme is introduced, followed by the mother's at 2:48. The mother's theme, although it has essentially the same rhythm as the goblin's and is also in B minor, is reversed in the direction of the phrases. The piece is built almost entirely around these three motifs, with the percussion almost continually emphasizing the first three beats of every measure.
The folkloric subject of the piece is completely typical of Dvořák. Although the program of the piece is extremely gruesome, the tone is nostalgic; you can almost tell that Dvořák just returned from a long trip away from his homeland. Pieces like this by Dvořák, Smetana, and Janáček are very influential representations of the Czech national identity.