TuneIn Radio is probably the most robust streaming radio app currently available on iOS. It'll be familiar to users of TuneIn.com, which aggregates radio stations from all over the world and streams them directly to your desktop through a browser. The TuneIn Radio app does the same thing, except it streams directly to your iPhone.
The TuneIn Radio app is very smartly laid out, with essentially all the core functions accessible right from the home screen. You can search for radio stations in a number of different ways: geographically, by category and ordered by trend.
Once you have selected a radio station to stream, it will load along with a graphic for the particular show that's currently playing. For example, if you were to load WNYC-FM 93.9 around noon, you would see a photograph of Brian Lehrer.
Above Brian Lehrer's portrait, you would see a share button that allows you to share on Facebook, Twitter and via email. To the left of that is a rewind button, which allows you to go back 10 seconds in the broadcast.
One of the neatest features in TuneIn Radio is the ability to record the audio stream you're listening to. Simply hit the red record button in the stream. You can retrieve your recording later in the recordings tab, accessible from the home screen.
TuneIn Radio also has a car mode feature that allows you to search for a select radio stations on the fly with a more dumbed-down interface intended for minimal distractions.