Also Conquest of Paradise for me! I had the tune randomly pop up in my head for well over a decade, probably close to two, without having any idea what it was. Every few years I tried finding out what it was, but to no avail. Online melody searches weren't that good, and when I hummed the melody to people or played it on the piano, people either had no clue or, at best, were like "that sounds familiar but I have no idea what it is". I even toyed with the idea that I had come up with the melody myself, though I did find it unlikely.

I can't describe the happiness I felt when I finally discovered the actual song when I once again tried finding it, this time by humming into Google's music search thing