The library-provided Overdrive and EbscoHost services are available and free with your library card. You can download them to your pc or eBook reader, and the books automatically return themselves so you can read them on vacation and not have to return them to the library.
Project Gutenberg (which contains public domain books) is a good choice for free downloads. PG offers most of its books as free Kindle books, as well as in the ePub format. (You can download free Kindle books directly to your Kindle by pointing your Kindle browser to m.gutenberg.org). It also has a useful guide to downloading books from this site.
Epubbooks offers Kindle and ePub books available as free downloads. iBookNook has these downloads also and currently on the site is a recent post that lists 50 classic books that are available to download.
Amazon has free Kindle books that may be on your reading list, and Barnes and Noble ran a promotion for a while for free “classic” eBooks but this has apparently ended.
Google offers free eBooks although they don't organize the free ones as a browsable group. Many classic books are offered for free.
I've included this link to free eBooks for Nook, and this link to free eBooks for Kindle (includes information on a free way to convert eBook files to Kindle) as additional resources.
If you only find a book in PDF format and have a real desire to read the book in the ePub format (here’s an article on the advantages of reading an eBook in the ePub format) for $23.95 you can download a PDF to ePub converter.
We'll be happy to help you. If you need help finding or downloading free eBooks, contact the library reference department at 412-828-9520 ext. 215 or send an email to firstname.lastname@example.org