The SitesProject Gutenberg: Made up of a large group of volunteers, Gutenberg hosts tens of thousands of free books in various formats, including Kindle, PDF, and plain text. You can usually find any notable text written in English from before about 1925, as well as some more modern ones that are no longer in copyright. Project Gutenberg Australia has books from 1955 or earlier. They don't have as many books as the American site, but if you want something newer, they are a good resource. The University of Adelaide also has some more recent books that Gutenberg lacks.
|Wm. Caxton from The Graphic, 1877|
However, I've found that for many of their books, while the PDF version will be fine, the other formats will often have problems with formatting and spelling as a result of their computers trying to turn pictures of book pages into words and letters. They also put up other types of files, such as music and videos.
There is also Google Books, which lists pretty much every book ever written--though only some of them are available for free. To find the free ones, search for an author or title, then press enter. When the results come up, click on 'search tools', then 'any books', then select 'free Google eBooks', and it will show you a list of free books related to the author or title you searched for. Once you've selected the book you want, go to the right of the screen and click on the little gear, which will give you the options do download it as a .pdf, .epub, or plain text. You can often read more recent articles and collections this way, even if it doesn't let you download them as eBooks.
|Kipling - With The Night Mail|
Of course, when you're dealing with foreign authors like Chekhov, there's always the caveat that the translations you can get for free are quite old, and as such, don't tend to represent modern scholarship and expertise. Indeed, it can be a problem in many Victorian translations, which tended to bowdlerize their subject matter in order not to offend strict Victorian sensibilities. When reading a work in translation, it's always worthwhile to read up on different translations and pick the one that works best for you and your needs as a reader.
Amazon also has a selection of free eBooks available for Kindle, though if you get the computer program Calibre, you can change Kindle files into any other type of eBook file (and vice-versa). You can also check out ManyBooks and OpenLibrary. I know they have thousands of free books available, but I haven't used those sites yet. It is also possible to get free ebooks on loan from your local library.