I've always thought if the universe had an audible soundtrack, it would sound like Bach. All of the other big hitters are up there of course, when it comes to the old masters, with a particular emphasis on Debussy, Mozart, Tchaikosky and, as much as many classical music lovers look down on him a bit, Strauss II. I do love a polka.
With modern composers, especially soundtracks, all of the ones mentioned so far figure highly, as well as Basil Poledouris, if only for his soundtrack to Conan the Barbarian. Whatever your opinions of the film, it's impossible to call the soundtrack anything other than a work of genius, as was his score for Lonesome Dove; The Hunt for Red October was none too shabby, either.
How stringently are we defining 'Composer'? Because I'd add Gershwin, Bernstein and maybe a dozen jazz composers to the list, mostly from the bebop era through to the middle of the free period; start with Parker and Davis, then work through the big names until you get to Benny Green. Then stop. I find modern jazz a bit too noodly and somewhat limp.
I like music a lot. I can never call one artist or piece my favourite. It always boils down to lists, with me. Hence claiming almost everyone else mentioned, plus my few additions.
* Correction - Carpio diem