The problem with recognizing James Horner is you're usually recognizing one of the countless classical, romantic and modern composers he's ripped off.
I agree on these other composers (especially Herrmann - the ultimate: three - maybe two - notes and you know it's him) and would add:
Danny Elfman - another self-taught guy who is really good and one of the few Americans after John Williams to have a distinctively different sound
Preisner - he has adapted Herrmann's use of motifs in an original, even more minimal way with an extreme, sometimes blatant expressiveness
Georges de la Rue - his music for Truffaut's films has a recognizable combination of simple motifs and understated light quality
Nino Rota - his melodies and crazy, humorous combinations of pop with orchestral sounds as in Fellini have never been equalled
Ennio Morricone - though the spaghetti westerns are only part of his output their sound is totally original, even weird in a sense
Max Steiner - his music almost screams at you STEINER! STEINER! STEINER!
Erich Korngold - another instantaneously obvious one with his luxuriant romanticism
Elmer Bernstein - with his somewhat Coplandesque vigor, but somehow different (and maybe even better)
Alex North - his way of handling the orchestra has a certain transparent quality to it no one else has - i.e. "Spartacus" or the original "2001" score
Maurice Jarre - his chromatic harmonies and melodic emphasis
John Barry - the combination of great, extended melody-writing and a simple yet strong orchestration, with a lot of use of short motifs somewhat similar to Herrmann
I agree on these other composers (especially Herrmann - the ultimate: three - maybe two - notes and you know it's him) and would add:
Danny Elfman - another self-taught guy who is really good and one of the few Americans after John Williams to have a distinctively different sound
Preisner - he has adapted Herrmann's use of motifs in an original, even more minimal way with an extreme, sometimes blatant expressiveness
Georges de la Rue - his music for Truffaut's films has a recognizable combination of simple motifs and understated light quality
Nino Rota - his melodies and crazy, humorous combinations of pop with orchestral sounds as in Fellini have never been equalled
Ennio Morricone - though the spaghetti westerns are only part of his output their sound is totally original, even weird in a sense
Max Steiner - his music almost screams at you STEINER! STEINER! STEINER!
Erich Korngold - another instantaneously obvious one with his luxuriant romanticism
Elmer Bernstein - with his somewhat Coplandesque vigor, but somehow different (and maybe even better)
Alex North - his way of handling the orchestra has a certain transparent quality to it no one else has - i.e. "Spartacus" or the original "2001" score
Maurice Jarre - his chromatic harmonies and melodic emphasis
John Barry - the combination of great, extended melody-writing and a simple yet strong orchestration, with a lot of use of short motifs somewhat similar to Herrmann