Project Gutenberg is an oldie but goodie when it comes to finding free ebooks. These books are in the public domain, at least in the US, and can be read online or downloaded. Some may even be compatible with the Kindle. This is a relatively small collection so far at 38,000 titles, but it does offer a wide range of books in languages other than English.
Open Library is another great resource. It's kind of like Wikipedia, where anyone can add a title or fix records already online. So far it has over 1 million books going back to the year 1000 or so. Clicking on a title gets you the publishing history, and you can choose which edition to read online. Again, you might be able to send a copy to your Kindle. This site is part of the Internet Archive project, which is like a massive Library of Congress, trying to preserve everything from websites to video and audio files, music, and texts. The interesting thing is, not everything in the text section of the Internet Archive is fully available in Open Library. The Archive still gives you the option to download books or read them online, so if what you are looking for isn't in Open Library, try the Archive (which has 3.3 million titles).
Digital Public Library of America says it will "provide a Google-Books-like experience but without the hassles of lawsuits" when it goes live in April 2013. It will try to bring together all those listings of ebooks available online, to be the go-to catalog or national digital library for anyone wanting to download or read online.
Even with Google Books, which scanned and digitized hundreds of thousands of pages without bothering about coypright, you aren't going to be able to read a current, popular ebook for free, though you may find a way to purchase one should an ebook version exist. But with the sources listed here, you can find some good research material without needing to visit a physical library building or paying to download a file.