I think this is too subjective to answer. Every human is different and has different likes/dislikes. Even composer's who are considered masters have slammed other's who are considered masters throughout history. One day as a race we might learn to see that we all simply differ and to respect one another's tastes whether it be in music or elsewhere, without judegment.
I'm as guilty as the next person in this area unfortunately, but i'm trying to keep an open mind as I listen to things.
I think it is easy to tell a good composer from a bad one (or one that is a newbie or just starting out). What is more subjective is how to tell if a composer is great or a master. It all depends on how history records them, how hard they work, their knowledge of music theory and the mechanics of music, how much they know about various instruments' capabilities, etc.
Another important factor seems to be innovation. What does the artist do that is new? And does it work?
Now back to the original question, what makes a good composer...
1.... Knows his or her stuff. In other words, music theory. Gotta know the rules before you can break them.
2.... Good knowledge of what all musical instruments (except the obscure ones) can do.
3.... Good skill in ear training. (How else can one take the melodies heard in their head and put it on paper)
4.... Individuality. The desire to not compose like Mozart, Beethove, John Williams, etc.
The rest is more subjective, because who can say whether a melody is bad are good.
DMA Student and Teaching Asst in Music Theory/ Composition at the University of Miami Personal Website
One of my composition teachers in college told me this story. When he was studying composition (in college or grad school, I don't remember which), he lost confidence and decided he was no good, and that he would never compose again. He gave up composing for a very long time.
Then one day on a whim he went to a conference where John Cage was speaking. After the conference, he introduced himself to Mr. Cage, saying something like "I used to be a composer, but I stopped because I was no good."
John Cage's response "Of course you're a composer. You're alive!"
At that point he jumped right back into composing, studied with Stockhausen, got a Doctorate, and now has taught at major universities in the USA and Turkey. He's one of the more innovative and energetic composers I know.
A simple answer may be a composer that is able to create something that pleases the audience and evokes an emotional connection. If only things were so simple.
This reminds me of a barroom discussion I had years ago with an artist friend of mine. I had recently finished college where I took a lot of art history courses. We were discussing the relative merits of art history, and he felt that it was a waste of time, because the appreciation of art should not require any knowledge on the viewers part. While I agreed with the concept, I argued that a knowledge of art history was essential to be able to judge a works value in relation to the collective body of what has come before. Is the artist adding anything to the collective, or just rehashing what others have done before? Taken to the extreme, If one were to paint a copy of the Mona Lisa, and show it to someone that had never seen the original, they may consider it a masterpiece, but would it make the painter a great artist?
I guess what I am trying to say is that a good composer is not just the ability to create a pleasant composition, because it may just be a composition that paraphrases the work of others. Although come to think of it, that may be the distinction between a great composer and a good composer- the good composer creates pleasant compositions, but breaks no new ground, and the great composer has his/her own voice. Hmmmmmm
These are music students who asked an academic question. Training, lessons, learning to read and write music, a good ear (maybe two) understanding of what is popular with the listeners of their times. Yes? No? Maybe Not?
A good composer takes something that already exists and uses his skill / intelligence / experience / knowledge to create something new and interesting out of it. He does not feel the need to reinvent the wheel on each composition, but always strives to improve himself and his music. He always tries to come up with new and interesting solutions/approaches to problems/pieces that already exist or have been done.