Free books on the web fall into a few different categories:
Older Books that are no longer in copyright
Many books published before 1923 (and some published later) are no longer in copyright.* There are many projects on the web that provide the text of older books or scanned images of older books. The massive Google Books project scanned both public domain and copyrighted books. Often when the book is in the public domain you can get the full text on Google Books. Google Books is great for searching (since it searches the entire text), but other sources listed here may provide books in a form that is easier to read.
Open Access books
These are books that the authors and publishers intend to share for free. Many of these are published by university presses, libraries, museums, and other academic organizations. Some of the best open access books are already included in Esearch.
Books and other documents produced by governments
By law the U.S. government can not copyright the books and other documents it produces. A very large number of works published by the US government are made available on the web. Many of the most useful US government publications can be found in Esearch.
Books by other government entities or intergovernmental organizations might be copyrighted, but they are still often made available free on the web.
*The rules for when a book becomes "public domain" are a bit complicated, so this isn't always the case.
An internet search for the title in quotes with the words full text may find a classic book you are looking for [example Google Search: "Ragged Dick" "full text"]
Below are links to sites that offer full text of classic books.