When someone clicks on your mp3, it’s up to them what happens.
As far as I know, you can’t just stream MP3s from your site unless you have something like a Shoutcast server. Otherwise, people have options.
If they have their browser set to automatically play stuff, then it will. My browser is set to ask me whether or not to download the file or to play from the site.
Then the end user’s computer figures out what program they have set to play MP3s. Mine’s configured to play them with windows media player. Others might have WinAmp, quicktime or real player or something else.
Most people have some sort of component installed that is set to play MP3s (even if by default). If you have a lot of MP3s you might want to provide a link to some free players. Here’s some links you can provide, and they can choose:
windows media player (windows)
real player (multi-platform)