Here's a brief description from their website:
midomi is the ultimate music search tool because it is powered by your voice. Sing, hum, or whistle to instantly find your favorite music and connect with a community that shares your musical interests. Give it a try. It's truly amazing!
I was skeptical until I tried it. I plugged in my microphone and sang a couple of bars of "Happy Birthday", and sure enough, midomi figured it out and provided links to recordings of other midomi users singing the song, and to professional recordings available for purchase.
Then I sang the first phrase of the "Star Spangeled Banner", and BINGO! Another match! My hummed rendition of "Na na, hey hey, kiss him goodbye" didn't yield a correct match, but remarkably, my WHISTLED version of "Billie Jean" brought up a link to the Michael Jackson original, cued up to the phrase I had just whistled!
It really is amazing! Give it a try.