You can always play stations by typing the station name into your browser like this:
That would play wfmu.
This would play a random station:
To get a playlist of all stations:
You can add an r to that to get a playlist of all stations in random order.
To get a playlist of stations that I think are the best ones, try goodradio.org/best. You can add an r at the end to make the list be in random order. Feel free to suggest other stations to be added to this list.
A good tip is to drag one of those to your browser's bookmark bar. Then just click it to hear that station.
Note each of the above returns a pls file. If your application needs direct access to the stream, which you probably do if you're trying to play a stream from a cellphone, you might try this:
Note the word "stream" in the URL. Since that's a lot to type from a cellphone, here's a shortcut:
Note the dash before the station name instead of the word "stream".
You can see what stations are available by having a look at the database.