Renaissance: Des Prez, Machaut
Intermediary: Monteverdi
Baroque: Handel, Purcell
Intermediary: Gluck, D. Scarlatti
Classical: Haydn
Intermediary: Schubert
Romantic: Liszt
20th/21st century music is where it gets complicated. You could name school after school after school. Schoenberg, Stravinsky, Cowell, Ives, Varese and Debussy are probably the most important early 20th century composers. Babbitt, Boulez, Cage, Xenakis, Schaeffer, Stockhausen and Pousseur are probably the most important of the Darmstadt Era. Ferneyhough, Dufourt, Radulescu, Lachenmann, Kurtag, Kagel, Ablinger and Stabler are probably the most important of the last 40 years or so. Neoclassicism and minimalism aren't really "important" in the sense of the forwarding of music, but composers instrumental to their creation are Enescu, Bartok and Prokofiev, and Riley, Reich, Part and Gorecki, respectively. Ustvolskaya, Gubaidulina and Schnittke are important figures in the late phase of Neoclassicism and deserve to be mentioned in their own right.
But if you really want to ask, "who is the most important person in contemporary classical music," the answer must be Pierre Boulez. Boulez's control over the contemporary music scene - as director of IRCAM and the Ensemble Contemporain, both of which are basically the ATM for many contemporary composers (ones he deems worthy, and that is where his power comes in) - is utterly dominant.