Early Music (?-500AD)
The Oldest Known Melody (Hurrian Hymn no.6 - c.1400 B.C.)
Here's an interview with Michael Levey, who is the lyrist who played the piece (which is written in cuneiform) and a link to his website which has many more beautiful songs from the ancient world.
Classical Period: ~1750 – 1825 AD (W.A. Mozart, Franz Joseph Haydn, C.P.E. Bach)
Romantic Period: ~1825 – 1900 AD (Ludwig van Beethoven, Franz Schubert, Johannes Brahms, Claude Debussy)
20th Century Period: ~1900 – 2000 (Maurice Ravel, George Gershwin, Igor Stravinsky, Aaron Copeland, Phillip Glass)
21st century music: 2000-present (John Corigliano, Eric Whitacre, John Williams, Jessie Montgomery, Jennifer Higdon)