Simple Radio (Pro version)
Compared to "TuneIn": The database of radio stations is not perfect, but this app is really simple and more intuitive: You see the status of the radio station at once, and you see at the same time recording is on or off.
Unlike "TuneIn" you can enjoy your recording ONLY from the beginning; you cannot jump to the position you like: The reason for minus one star.
[Addition, 2015-9-2:] How many times have I got to write a review?
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Simple Radio – Live AM FM App, v3.1.5