The players you need.

The first thing you'll notice when you start listening to live streams is lots of sites want you to download their custom player, which can be a pain and most of the time you really don't need them at all. I listen to lots of streaming audio in a day and these are all the players I use:

Winamp, RealPlayer*, Windows media player, and Quicktime.

• Realone... the Realplayer I use is a spam free version I got off the BBC site, it's the normal realone player but with less bloat then the player you get off reals website. Note after installing this player you'll want to go into the options and turn off all the extra 'bells and whistles' you don't want.
• Quicktime... apple has started to add bloatware to there player. But the link I supplied is quicktime without all the iTune junk.
• Winamp... is still my mp3 player of choice. When installing this player turn off all the extras you don't use apart from wanting to put links to itself all over your system it tends to install pretty clean. If you have an older version you may want to get the latest one here. It plugged up some security issues it had.
• Windows Media Player ... as for windows player this is the player I use the least. If you have windows os you already have this. But you may want to get the latest version.

Some sites also choose to use flash players or other webpage scripts to play the audio embeded in the web page. If you turn off javascript these players may not work.
You will also find sites that force you to get their custom player, I tend to avoid these sites. There's too much good audio to be bothered loading custom players all day!