The New York Times is currently running a "Top Ten Classical Composers" video series hosted by NYT chief music critic Anthony Tommasini. The videos are easily digestible, truly informative, and enjoyable--win, win, win--so I greatly encourage you to check them out. You may need to sign up for the NYT online to access the series, but signing up is free.
Read the article here, then watch the videos (more will be added through January 21st), and cast your vote! Related Arts Beat posts here.
Mine were Bach, Beethoven, Brahms, Mendelssohn (of course), Tchaikovsky, Debussy, Stravinsky, Prokofiev, Gershwin, and Copland, though I admit personal bias made my choices more than who I think is most important to Western classical music. Handel and Mozart would have made the list, in that case, at least.