British Library
The official British Library website allows you to search over 18.5 million records contained in 21 different databases! Whilst you cannot access texts online, it still contains a wealth of useful information.
The Complete works of Shakespeare
A comprehensive website about the works of Shakespeare, this site contains the complete texts of all his works from Hamlet to Othello. The site also includes an online forum about Shakespeare's works.
Electronic Text Archive
The Etext Archive contains a wide variety of works on subjects ranging from politics to poetry. Many of the authors are as of yet unknown and use the Etext Archive as a staging post for publish their works.
The Library of Congress
Perhaps the most famous library in the world, the internet version of the US Library of Congress contains a multitude of texts, diagrams, paintings and maps that can be accessed online completely free of charge!