The translators of the New International Version (NIV) and the Today's New International Version (TNIV) of the Bible have made an online version of this translation available on their website. It also contains a concordance, a bible dictionary and a audio bible. You can also search for scripture passages by verse or by keyword.
The United States Conference of Catholic Bishops website has made available an online version of the New American Bible (NAB). It contains a primitive search feature that lets you search for phrases.
The Knights of Columbus have made available an online version of the New Jerusalem Bible (NJB) on a Duquesne University sponsored website. The Duquesne University figured significantly during the early days of the Catholic Charismatic Renewal.
You can download a Bible to your mobile phone or PDA and read the Bible on the go. Some revisions are free, while you have to pay for the better translations such as the NIV.