I’ve wondered this, especially since once in a while someone notices that one song or another sounds like another different song or piece. Sometimes I’ll suddenly think of a snippet of music (usually in the shower or right before I fall asleep) and I wonder if that particular arrangement of notes have existed before. Here’s an article I found that provides a reassuring answer:
We won’t run out of new melodies any time soon. Although the number of possible melodies is finite, it is so very large that for all practical purposes, the supply of new tunes is infinite.
New Scientist, Could we run out of musical note combinations to create new melodies?
Chicken Little 
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