Shazam has been popular on iPhone for quite some time. Fire it up and the app will listen to the music playing and report back what the song is.
In iOS 8, however, Siri can access Shazam even if you don’t have the app on your phone. Just ask “What song is playing” or “What song is this”.
Unfortunately it might not work well in a noisy place such as a club if Siri can’t hear your request.