Full text is available for those books which are out of copyright and those which Google Books has permission to make openly available. Limited search capability, but you can filter results to open access titles by selecting Full view.
This provides public access to out-of-copyright titles. MIT has an institutional account that enables MIT affiliates to also access the full text of copyrighted works that are part of the MIT Libraries collection.
20 million freely available eBooks can be found here. These are out of copyright titles, but an additional 2.3 million modern eBook titles can be borrowed by those who set up their own personal account with Internet Archive.