Japanese Text Initiative   http://etext.lib.virginia.edu/japanese/index.html
Sponsored by the University of Virginia Library Electronic Text Center and the University of Pittsburgh East Asian Library, JTI is a collaborative effort to make texts of classical Japanese literature available on the World Wide Web; out-of-copyright modern texts are also included.  Designed for non-native speakers.  Can be searched or browsed by author or title and period.

Kokubungaku shiryōkan   http://www.nijl.ac.jp/contents/d_library/index.html
Includes the full-text of the old edition (Iwanami) of the Nihon koten bungaku taikei (100v. 580 works) plus the Nijūichidaishū (waka), the　Azuma kagami, the Eiri Genji and the tenbu section of Koji ruien.

Aozora Bunko   http://www.aozora.gr.jp/
Focuses on digitizing modern authors out of copyright, but also includes Japanese translations of Western authors.  Provides brief biographical information about the author, information about the text - where it was first published - as well as the source of the text that has been transcribed into html.  Available for download in several file formats.

Japan Literature net  http://www.jali.or.jp/
This is a site for people interested in contemporary Japanese writing (Tsutsui Yasutaka, Kobayashi Kyoji, and others).

Nihon Bungaku nado text files  http://www.ne.jp/asahi/nihongo/okajima/bungaku.htm
Largest collection of text files in Japan.  It includes free/fee files, so if you are wondering whether a text has been put online yet you should check here.  Organized by period - classical, medieval, early modern, modern, other.

J-Texts    http://www.j-texts.com/