There's no shortage of apps that will play any song you can imagine at any time. Radio Search Engine is a webapp that does it by searching for what's playing live on the radio right now. From there, it can build a playlist of other live streaming tracks for you.
Just type the name of a song, artist or radio program into Radio Search Engine, and it will scour the live feeds of thousands of radio stations across the globe to see where it's playing at any given moment. You can then create a custom station that will bounce around other stations in real time looking for new songs.
It doesn't work nearly as well as a service like Pandora, but it has a sense of urgency behind it since it's live. If nothing else, it's a really nice web player for radio stations that may well beat your local station's native offering.