The phrase "listen to music" is correct. Like JamalamaJ said, you don't need to define music with the definite article "the" since it is a concept. If you were to describe the music with an adjective such as "rap" or "rock" then the sentence would become "I like to listen to rap music." It still does not have the definite article because it is a concept. Another example of this type of sentence: "I would like to go to sleep." Again, you should not say, "the sleep" because it is a concept not a definite idea. If you were to talk about music in a specific place at a specific time, then you would use "the" to define music. This is used to distinguish between the general concept (music "in general") and the specific music in a specific place. An example is "Tonight, the music here is great."

"I like to listen to music." - You say this when you like to listen to music "in general." However, if you're talking about a specific kind of music with someone, then you can say "I like to listen to the music" - "the" is the specific kind of music previously mentioned already.