When I was a young teen, one of my friends gave me a floppy disk of midi song files she liked a lot but they mostly had names like "ANIME 2" so I had no idea where they came from. There was one on there I was particularly obsessed with but could never find. Then one serendipitous day, I did. It was The Destruction of Laputa from Castle in the Sky.
Edit: Or it was Sora from Escaflowne. There's been a few times I heard an instrumental or non-English song with no source to go off of.