Shazam (free)

Shazam is perfect for identifying that song you hear on the radio, but have no idea who sings it. All you need to do is to point your phone at a speaker (you'll need an Internet connection for the app to do its work) and you should get the results in a few seconds. And now it even identifies TV shows in the same manner. Of course, it can't find everything, but it's a great tool for discovering new and popular tunes.