Yes! Quite often. Songs, tunes, poems, stories.

I think a hidden part of our mind just keeps working on stuff, while we are awake as well as while we are asleep, like the stars are still there day and night. Between sleeping and waking some leakage can occur. Sometimes also when awake 'an idea come into our head'. It feeds into dreams more easily, and sometimes we remember those.

But it helps if it generally doesn't intrude into our conscious thought. Some minds may just be more leaky than others. The downside is that I am day-dreamy, absent-minded, have to work to focus on normal life. I manage OK, but at the wrong moment I have tell that intriguing new tune to go away.

Dreams I think are of differnt kinds. Some are coherent, and if rememebered can provide whole created events including music or song. Some of these do seem special, others much what we would compose when awake. Other dreams are incoherent. But I did once wake and write in the dark the revealed key to the universe. Next morning I read on the pad: "To tie an indefinte number of holes to a string vest, said the Professor."

Chris