…or at least my amateurish whistled imitation of it?
Wow, that sounds really familiar…unfortunately I’m blanking on it right now. I think it reminds me most of something I might have heard on a movie soundtrack, but I could be totally off on that. It also sounds vaguely like a hymn or Christmas carol that I can’t place at the moment. Hope someone solves this one for you soon, I’m eager to find out, too.
Got it! It’s Greensleeves! Or, alternately, it’s “What Child is this?” which is sung to the tune of Greensleeves.
Oooh… good guess, but not quite 
I thought there was a part of Greensleeves I might not’ve known, but I listened to the whole song and that melody’s not in it. It’s CLOSE though.
Wow, are you sure it couldn’t be “What Child is this?” I swear that’s all I can hear now when I listen to your whistling sample.
I just realized that whistling it without any tonguing makes it hard to tell the notes apart… my bad!
Hopefully this hummed version will have somewhat better-defined notes.
Edit: And yeah, as far as I can tell, you’re right that “What Child Is This” is the same melody as Greensleeves… unfortunately
Dang. Sorry, tried my best!
And if it helps, here’s my attempt to write it in musical notation (also available as a plain image if you don’t want to wait for the Flash editor to load). I’m not a musician, though, so it’s far from perfect.
And Cuckoorex, I certainly appreciate the attempt 
It might help if you could tell us where you heard it, or at least what genre it might be. Is it a vocal? Instrumental?
The only thing it reminds me of is Seal’s “Kiss From a Rose.” But that could be because you’re humming it in a similar way.
Rhythmdvl posted this page last year: musipedia
Links are embedded into the text, and the piano keyboard goes to an image of a keyboard you can play the notes on.