Monteverdi should most definitely be on that list, Handel too. They are both musical giants. Here’s my own choice.
A little opera-centric perhaps (it was all I could do not to squeeze Bellini, Donizetti and Verdi in!) but de gustibus and so on.
I don’t know enough about Morricone’s work. But Williams has worked widely and his music stands on its own.
Top 10 classical composers:
It saddens me to leave out Rachmaninoff and Franz Lehar, but I have to be a bit objective in my assesment. Since someone brought up Morricone and John Williams, I also have a top 10 list of film composers:
1/2: Jerry Goldsmith
1/2: John Williams (don’t make me pick)
3: Bernard Herrmann
4: Henry Mancini
5: Erich Von Korngold
6: Miklos Rosza
7. Enrico Morricone
8. Danny Elfman
9. Hans Zimmer
10. Camille Saint-Saens (though I suppose that’s more of a "lifetime achievement award for pioneering the genre)
…
…
…998. Will Sasso’s “Casio Keyboard” character from MadTV
999. James Horner. 
What does everybody think of Hildegard von Bingen? If the standard is “influential”, maybe not so much, but if the standard is genius and aesthetic appeal or effect on the listener, I’d say she’d have to be in the top ten. Especially since it was liturgical chant that first developed into the motets and chansons and what have you, and eventually into polyphony, classical opera and, uh, Christina Aguilera.
Just a thought.
In my experience, she’s very highly touted by feminists and female composers. Perhaps rightly so. But you’re guilty of a huge logical leap if you’re making the case that hildy was responsibly for polyphony. If it was Helmut von Bingen, IMO he’d’ve been a historical footnote.
Sorry everyone, about rehashing old territory (what is “classical” for the purposes of this thread). I blush-- I admit I had only read a few of the posts before I responded.
It will never happen again!!*
*uhhhh… yeah. Right… 