Who's everyone's favourite composer from each period of classical music?
You know this is hard to answer right?
For Early Music I pick a somewhat left-field choice: Nicolas Gombert. His turbulent volleys of sounds are like no one else.
For Baroque J. S. Bach is hard to avoid, but on balance I think Handel's achievement is greater: his works simply cover a wider emotional range.
The genius that shines brightest in the classical period is Haydn. People favor Mozart and I have no complain with that, but to me Papa Haydn is the man.
The early romantic period is backwoods to me; I just find it hard to tune to the highly subjective music of say Beethoven or Schumann. It took me a long time to learn to appreciate Chopin, and it is only though understanding his connection with the Classical period (rather than Schumann).
Brahms is a Big One, perhaps the BIGGEST on my estimation. The genius of Brahms is the way he organizes the musical discoveries of the arch-Romantics, and uses it in a less subjective, more purely-musical, manner.
When we arrive at the 20th century things get interesting, and it is far far harder to speak of favorites. Various composers have contribute uniquely to classical music: the expansion of the diatonic system (Debussy, Ravel); the pleasure of tone color for its own sake (again Ravel, also Scriabin and Zemlinsky); the justification of twelve-tone system not as an academic exercise but as a genuine expressive means (Berg, Lutoslawski); the irresistible, decadent allure of the massive high-romantic orchestra (Richard Strauss). And there are some favorites that simply cannot be pigeon-holed, such as Ralph Vaughan-Williams.
When it comes to the modern / post-modern period it is simply impossible to give an overview. Let's just say the composer I admire the most is Elliott Carter, and the one who touches me the most is Alan Hovhaness.
