I agree with most others here in that picking ONE is nigh on impossible. However, having said that, I've noticed with no small amount of interest that when pondering this very question, I'll tend to look backwards through the eras of Music History (ie, 20th Century, Romantic, Classical, Baroque, Renaissance, Medieval, Ancient) and I tend to work my through in a circular motion (hope that makes sense!). More often than not, I find that my aim still falls on the man who so perfectly bridged the gap from Classical to Romantic - Ludwig van Beethoven. For me, there are still few who come close to him in terms of mastery (and thoroughness) of compositional technique coupled with emotional depth, the latter of which paved the way for the Romantic and 20th Century "giants" to follow.
However, I should at least respect each era and note that I have definite favourites from each:
Medieval -Hildegard, Machaut
Renaissance - Tallis, Victoria
Baroque - JSB of course, Corelli, Vivaldi
Classical - LvB, Schubert
Romantic - Berlioz, Schumann, Chopin, Franck, Saint-Saens
Impressionist (as a link from Romantic to 20th Century) - Debussy, Satie, Ravel
20th Century - Holst, Vaughan-Williams, Stravinsky, Messiaen, Alain, Vierne, Bartok, Ligeti, Shostakovich, Rachmaninov