The Composers

Classical Era forerunners:

Joseph Haydn  (1732 - 1809)  Austrian -  inventor of the piano trio 
Muzio Clementi  (1752 - 1832)  Italian → British  "Father of the Piano"
Wolfgang Amadeus Mozart  (1756 - 1791)  Austrian  The Piano Concertos 
Jan Ladislav Dussek  (1760 – 1812)

Transition into the Romantic Era:

Ludwig van Beethoven  (1770-1827)  German  Beethoven's Piano Works
Johann Nepomuk Hummel  (1778–1837)  Austrian

Anton Diabelli  (1781–1858)  Austrian  (Beethoven - 33 Variations on a Waltz by Diabelli) 
John Field  (1782–1837)  Irish → Russia
George Onslow  (1784–1853)   French  (example: Piano Sonata for 4 Hands)
Friedrich Kalkbrenner  (1785–1849)  German >→ Paris  (Example:  Piano Concerto #1  in D minor)
Carl Maria von Weber  (1786–1826)  German

Jan Václav Voříšek  (1791–1825)  Bohemia
Carl Czerny  (1791–1857)  Austrian  (His piano studies (listen) are still used today)
Ignaz Moscheles  (1794–1870)  Bohemian Jew  (example: Etudes caractéristiques) 

Franz Schubert  (1797–1828)  Austrian
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The Romantic Era proper:

Joseph Christoph Kessler  (1800–1872)  German  (examples of Preludes, Etudes, and more)
Amédée Méreaux  (1802–1874)  French  ("Bravura" étude, Op. 63 No. 24)
Henri Herz  (1803–1888)  German → France  (example)
Mikhail Glinka  (1804–1857)  Russian
Fanny Mendelssohn  (1805–1847)  German-Jew  (example)
Felix Mendelssohn  (1809–1847)  German-Jew  Songs Without Words (1829-1841)

Julian Fontana  (1810–1869)  Italian/Polish  (sample)
Frédéric Chopin  (1810–1849)  Polish → France 
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Robert Schumann  (1810–1856)  German
Clara Schumann  (1819–1896)  German
Sigismond Thalberg  (1812–1871)  Swiss → Austria
Charles-Valentin Alkan  (1813–1888)  French Jew
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Franz Liszt  (1811–1886)  Hungarian

Stephen Heller  (1813–1888)  Hungarian (forgotten) (samples) 
Adolf von Henselt  (1814–1889)  (example:  Sergei Rachmaninoff playing Henselt's If I Were A Bird)
William Sterndale Bennett  (1816–1875)  English
Édouard Wolff  (1816–1880)  Polish
Alexander Dreyschock  (1818–1869)  (example: Revolutionary Etude)
Henry Litolff  (1818–1891)  (Mostly known for Scherzo from Concerto Symphonique #4)

Thomas Tellefsen  (1823–1874)  Norwegian
Bedřich Smetana  (1824–1884)  Czech  Six Characteristic Pieces (1848) 

Louis Moreau Gottschalk  (1829–1869)  American 
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César Franck  (1822-1890)  Netherlander (Belgium) 
William Mason  (1829–1908)  
Anton Rubinstein  (1829–1894)  Russian  Piano Concerto #4
Hans von Bülow  (1830–1894)  German / Bohemian  (example: Impromptu for Piano "La Certa")  
Jan Gerard Palm  (1831–1906)  Curacao  (example: El 18 de febrero)
Johannes Brahms (1833–1897)  German
Camille Saint-Saëns  (1835–1921)  French  Piano Concerto #2
Mily Balakirev  (1837–1910)  Russian   Islamey  (1869)
Władysław Żeleński  (1837–1921)  Polish  (example: Grand Concerto de Concert) 
Józef Wieniawski (1837–1912)  Polish   (example: Piano Concerto in G minor, 1858)
Modest Mussorgsky  (1839–1881)  Russian  Pictures at an Exhibition (1874)

Pyotr Ilyich Tchaikovsky  (1840–1893)  Russian
Emmanuel Chabrier  (1841–1894)  French
Antonín Dvořák  (1841-1904)  Czech
Giovanni Sgambati  (1841–1914) Italian  (example: Piano Concerto, Op 15)
Carl Tausig  (1841–1871)  Polish  More known as a very great pianist than a composer. 
Edvard Grieg  (1843–1907)  Norwegian
Gabriel Fauré  (1845-1924)  French
Ignacio Cervantes  (1847–1905)  Cuban  Influenced Cuban music  (example: Danzas Cubanas)

Xaver Scharwenka  (1850–1924)  German  (example: Piano Concerto #4, 1908)
Leoš Janáček  (1854–1928)  Czech
Moritz Moszkowski  (1854–1925)  German Jew  (example: Etude in F major, Vladimir Horowitz, piano)
Pavel (Paul) Pabst  (1854–1899)  Prussian  (example:
Ernest Chausson  (1855–1897)  French
Cecile Chaminade  (1857–1944)  French  (example: Pieces Romantiques, Op. 55, 1890) 
Sergei Lyapunov  (1859–1924)

Edward MacDowell  (1860–1908)  American
Isaac Albéniz (1860-1909)  Spanish  Suite Iberia 
Anton Arensky  (1861–1906)  Russian   two piano trios and a piano quintet.
Claude Debussy  (1862-1918)  French
Eugen d'Albert  (1864–1932)  (example: Piano Concerto, Op 15, 1881)
Alexander Gluzunov  (1865-1936)  Russian 
Jean Sibelius  (1865–1957)  Swedish
Erik Satie  (1867-1925)  French
Enrique Granados  (1867-1916)  Spanish
Amy Beach  (1867-1944)  American
 
Alexander Scriabin  (1872 - 1915)  Russian Sonatas 5,6,7  (transitional)
Sergei Rachmaninoff  (1873–1943)  Russian
Charles Ives  (1874-1954)  American
Maurice Ravel  (1875-1937)  French 
Manuel de Falla  (1876-1946)  Spanish
Charles Tomlinson Griffes  (1884-1920)  American
Heitor Villa-Lobos  (1887-1959)  Brazilian