A good way to access the NRSV Bible online is through BibleGateway. This site allows you to look up verses in a variety of translations, including the NRSV.
Some other sites that feature an online version of he NRSV include Oremus Bible Browser and Bible Study Tools. These sites all accommodate searches for specific verses and passages.
Published in 1989, the NRSV is a popular translation with academics and leaders of the church. In addition to the traditional Protestant cannon, the translation also includes the Apocryphal books used by Catholic and Orthodox Christians. One reason for the popularity of the NRSV is its adherence to a literal translation of Biblical passages.