This article is from the Anime Music FAQ, by Ru Igarashi with numerous contributions by others.
First you need software. Some of the more popular ones are listed.
RealMedia/RealAudio
OS: Unix/Linux,Mac,Windows
RealPlayer - http://www.real.com
Streaming MPEG (including M3U and PLS)
OS: Unix/Linux
XMMS - http://www.xmms.org
FreeAmp - http://www.freeamp.org [note: for those who want software that also plays CDs, this uses MusicBrainz instead of freedb.org for CD database]
RealPlayer - http://www.real.com
OS: Mac
iTunes - http://www.apple.com/itunes/
Musicmatch Jukebox - http://www.musicmatch.com/home/
MacAmp - http://www.macamp.com
RealPlayer - http://www.real.com
Player365 - http://www.live365.com (tuned for live365) [see http://www.mp3-mac.com/Pages/MP3_Players-Mac.html for more]
OS: Windows
Winamp - http://www.winamp.com
Musicmatch Jukebox - http://www.musicmatch.com/home/
FreeAmp - http://www.freeamp.org [note: for those who want software that also plays CDs, this uses MusicBrainz instead of freedb.org for CD database]
Player365 - http://www.live365.com (tuned for live365)
iTunes - http://www.apple.com/itunes
Then you need some broadcasters, some of which are listed later in this document. Some will allow you to connect directly to a broadcast (i.e. you can start up the player without the browser and drop the address right in), others work through a service like Live365.com (i.e. it might be more convenient or necessary to access it via browser).
If you need a browser, you need to set it up to use the audio software. In your browser's applications/helper list you need to add entries for m3u (audio/x-mpegurl and audio/mpegurl) and pls (audio/x-scpls), if they aren't already there.
Keep in mind that internet radio broadcasters technically are supposed to be licensed (for copyright), so if you are fussy about that sort of thing, look for stations that have paid the copyright fee (i.e. through ASCAP, JASRAC, or similar).
 
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