I like Xiialive, because I can use my headphones' inline remote button to switch my favorite stations. I use V3.1.3, newer versions have trouble with the remote button. There are numerous stations including FM radio all around the world and online radio (SHOUTcast), in all languages including Chinese and Cantonese.
There is even a RadioReference plug-in that allows for listening to public radio such as police and fire etc. And you can add your own content if you know the URL. When you search for a station, set the correct directory: UberStations (local FM), SHOUTcast(online) and RadioReference (public).
You can set easily a sleep timer and wake-up alarm. There is an EQ with many presets, and bass boost and virtualizer dials.
It simply has everything you need for listening.
Like FM, not all broadcasts are the same audio quality, some are poor and some are super. Some of my favorites:
TheJazzGroove.com - the best audio quality and the right type of jazz.
All Classical Portland - the best audio quality classic music, although only 96K.
100.7 WZLX - the best classic rock.
KRVM-FM - the best variety.
CrystalRadioBeautifulMusic - the best easy listening.
Free China Radio - Very interesting talk in Chinese.
For music saved on my phone, I use the Clean Music player. It does not have any extra fat like other players.
So, these two great players are on my phone's home page, for online and local: