Hmmm, some very personal factors involved in this answer. The first classical composer that I can remember touching me deeply was Jean Sibelius (I used to lie on the floor in front of my parents' console record player listening to "Swan of Tuonela"). In the many years since then, the list of favorite composers has expanded a lot, and now includes (in no particular order):
1. Mozart (extraordinary range of compositions, and even his earliest works are good -- the late ones border on sublime);
2. Johann Sebastian Bach
3. Ludwig von Beethoven
4. Johannes Brahms
5. Archangelo Corelli
6. Antonio Vivaldi
7. Richard Wagner
8. Franz Liszt
9. Frederick Chopin
10. Antonin Dvorak
11. Anton Bruckner
12. George Frederick Handel
13. Peter Tchaikowsky
14. Camille Saint-Saens
15. Felix Mendelssohn
16. Jean Sibelius
1. Mozart (extraordinary range of compositions, and even his earliest works are good -- the late ones border on sublime);
2. Johann Sebastian Bach
3. Ludwig von Beethoven
4. Johannes Brahms
5. Archangelo Corelli
6. Antonio Vivaldi
7. Richard Wagner
8. Franz Liszt
9. Frederick Chopin
10. Antonin Dvorak
11. Anton Bruckner
12. George Frederick Handel
13. Peter Tchaikowsky
14. Camille Saint-Saens
15. Felix Mendelssohn
16. Jean Sibelius