To preface, I'm a musician; I've been playing the cello for roughly 10 years (started when I was 7). I'm also somewhat of a classical music nut (with a preference for late romantic to early modern era music); so I can say with confidence, that you're question is just simply too hard to give an answer to.
Classical music has changed so much over it's history that one really can't compare the likes of J.S. Bach to the likes of Shostakovitch or Bartok; they're simply too different. I can however name my favorite composers during various periods of classical music.
Baroque Period: As a cellist I have to say J.S. Bach. If it were not for his six suites, the cello would have a much smaller solo repertoire; also the TV shows and movies wouldn't have a go to piece to have characters "play" (Prelude to Suite #1)
Classical Period: Haydn, hands down. His work ranging from his cello concertos to his Kleine Orgelmesse (Little Organ Mass in B-Flat) are some of my favorite pieces to preform and to listen to. Hearing the finale to his cello concerto in C is what made me decide to play the cello over the violin, viola, trumpet, clarinet, etc.
I split the Romantic Period into Early and Late periods.
Early Romantic: Schubert. I can't pinpoint what it is that I like about his style, but it just stands out to me when compared to Beethoven, Weber, etc.
Late Romantic: Tie between Rimsky-Korsakov (for Scheherazade) and Elgar (for his cello concerto in E). Those two pieces remain the only pieces of music that have brought me to tears. The Elgar is a particularly emotional piece for me seeing as I was working on it when I had to put my cat/best friend down; I threw myself into the piece as soon as I lost him.
Modern Period: Tie between Dimitri Shostakovich and Sergei Prokofiev. Once again I really don't know why, but there's something that just makes them standout to me.
-Don
EDIT: to clarify, I did not vote in the poll, because there is no option which suites my stance on the issue.