Here are a couple of ways to listen to the Bible online.
http://www.mp3bibleplayer.org/ - As I understand it, this website and its content was developed by Calvary Chapel in Costa Mesa, California where Chuck Smith is the Senior Pastor. One nice plus is that they have a small, free program that you can download to your computer that allows you to bring up a small window that allows you to select what passage you want to listen to. The only drawback is that they only provide the New Living Translation, the King James Version, and a popular Spanish translation, but not the New International Version.
http://www.biblegateway.com/resources/audio - This takes you directly to Biblegateway's audio Bible page. Select your language, the passage you want to listen to, and ... voilà! ... you're in business!
If you would like to have the actual mp3 audio files, you can download them online (even specifying which particular book, etc., if you do not want to pay for the whole Bible) so that you can use them on your ipod, for instance. Here is one way to do it: http://www.listenersbible.com/productlisting.html?m=M Alternatively, I know that at one time Greg Laurie's ministry was offering a free version of Calvary Chapel's Bible audio cds for only the price of shipping and handling: www.greglaurie.org I did not find it currently listed on their website, but it is worth a email to them to see if they have any more available. There are also many commerical version widely available in Christian bookstores.