There are a variety of websites for listening to the Bible online, including Bible Gateway and The Streaming Bible. Each of these sites offers various Bible translations to choose from, including the New International Version, King James and American Standard.
The Bible Gateway website allows the selection of a Bible translation from a drop-down menu and the choice of a specific book and chapter of the Bible. The Streaming Bible's website lists out the translations that they offer, and provides a detailed description of the history behind each translation. Other options for online audio include the Talking Bible's site, which offers the choice of Biblical translations in numerous languages.