I encourage my students to use the NRSV translation. The best site for browsing this translation is the Oremus Bible.
Although they do not have the NRSV, another great resource for various translations (in other languages as well) can be found at BibleGateWay.com.
The blueletterbible.com offers various translations, and even has a browser for the Greek and Hebrew Bibles with word for word translation and concordance. While the Greek and Hebrew texts are not the latest scholarly texts, and the concordance is based upon the KJV's textus receptus, this is a fantastic resource of public domain materials for the novice and resource poor expert.
Another good resource for public domain materials (mostly older) available for Bible Study can be found at the World Wide Study Bible.