There are no composers every work of whose affects me on some level, but the vast majority of the works I've heard by my four favourite composers fall into that category; between them, they have written a significant number of the pieces I find most moving. And those four are Chopin, Debussy, Mahler, and Shostakovich. Admittedly, all four have written pieces I don't like very much or even outright detest (Debussy somewhat more than the other three), but they have written so many of my favourite pieces (taking just two by each, Scherzo No.4 and the Barcarolle, the Images and the Ballade, the second and fourth symphonies, and the E minor piano trio and first cello concerto (especially the slow movement)) that I could, and sometimes do, listen to pieces only by one of those four for hours on end.
Topic: Which Composer speaks to you?