You have a number of options. The library is the main source for current titles. See Shopaloic's comments on borrowing times. You can also check the author's and publisher's websites, since they may be giving away promotional copies. (A few authors even give away their books, depending upon other forms of revenue.)

Kobo's shop also offers free books, some being promotional and some being public domain. MobileRead and Project Gutenberg also offers free books, of the public domain variety.

If you want to try searching for books from other sources, use terms like: "public domain" or "creative commons" in place of the word "free".