Here are some (legal) sites that offer free online books.
The Online Books Page (University of Pennsylvania)
Google Books (click "Free Google eBooks" after you have done a search to show only the free titles you can read in their entirety online).
The Internet Archive:
HathiTrust Digital Library
Europeana (digitized books from European libraries + other material)
There are also many "specialized" free ebook sites that cater to one particular genre, such as fanfiction, open access textbooks, or early modern English literature. They are easy to find via a Google search.
All the sites to which I've linked comply with local copyright law in the country in which they are hosted. Except for Europeana, that would be the United States. They mostly contain public domain material, along with other material made available with the consent of the copyright holders.
Copyright laws vary from one country to another. A book hosted by Project Gutenberg that is public domain in the United States is still copyrighted in Europe if its author died less than 70 years ago. So the onus is on you to make sure that any book you read online or download through one of these sites is really legal in your country.
Happy reading! Taken together, the sites to which I linked host several million unique books. That should keep you busy for quite some time!