Midomi is a music database that allows you to search for songs by humming or singing a few bars. I heard about it over two years ago on Lifehacker. Then my dad reminded me about the site over the holidays and I went back to look at it.
The Midomi database/software was able to identify popular songs (e.g. "A Little Respect" by Erasure) and it even identified Chinese songs (my sister tried it). If you register for an account, you can contribute to the database by choosing a song you know well and singing into your microphone. I sang "How long has this been going on?" by George Gershwin and my sister gave a stirring rendition of "Twinkle twinkle little star."
Midomi is an example of "query-by-humming" software. There are other research projects underway to improve this software.