For work that is in the public domain, there is always Project Gutenberg. The site has more than 60,000 books, and you'll be familiar with many of the titles. It sometimes takes a bit to navigate the site, but they're updating, and there's a lot to see there, so I recommend roaming around the site for a few minutes to find your way around. They also have lists of the Top 100 Books of the Month, and if you click through to the new beta website, there are the top 100 books/authors of yesterday, the last seven days, and the last thirty days. A quick glance at yesterday's top 100 included works by Jane Austen, Charles Dickens, Louisa May Alcott, Robert Louis Stevenson, Jonathan Swift, Arthur Conan Doyle, the Bronte sisters, Oscar Wilde, H. G. Wells, Edgar Allan Poe, Jack London, and Mark Twain, among others.
If you're looking for something more contemporary, there are actually books whose authors have priced them as free. Often these are promotions, designed to tempt readers to buy the rest of a series or other books by the author. Either way, there's a wealth of material out there. Below are some places you can find those books and how to go about it.
Smashwords - at the top of the main Smashwords page, you can do a general search of all the free books on the site. Just click on Free in the second row (you can also choose the length in the third row). If you'd like to limit to books in the genre you're interested in, choose your genre in the left hand column and then click on Free. The books on Smashwords are in various formats, so you're probably in good shape no matter what kind of reader or computer you're using. You do have to register to use Smashwords, but I've been with them for years, and they've never sent me annoying emails.
Alternatively, you can go to this page, which lists a few categories with free books along with Today's Top Free eBooks.
Last of all, you can try this page, which appears to list all of the free books (not broken into categories) available that day.
Amazon - Amazon has a page titled Cheap Reads for Kindle: Free and Low Priced Reading Options. If you want only free as opposed to low-priced, set the search option to Sort by: Price: Low to High. At first glance, it appears that there are only two ways to break the 400 pages of books into divisions, Kindle Short Reads and Kindle eBooks, but if you click on Kindle Short Reads, you can drill down further based on projected time to read and number of pages. If you click on Kindle eBooks, you'll find genre categories. Unfortunately, I didn't find much of a selection when drilling down that way. That's often a failing of Amazon, I've found. You know that what you're looking for exists, but once you start setting parameters, not everything that fits those parameters is visible.
A better way, I've found is to go to the Kindle eBooks page. From there, scroll down the left side to your category of choice and click through. From there, scroll to the bottom of the page to where the books are listed vertically (as opposed to those nice horizontal categories at the top). Then choose Sort by: Price: Low to High. The free books will show up first.
If you're looking for book deals (as opposed to free), go to the Kindle Book Deals page.
Bookbub - go here for their daily deals.
eReaderIQ - eReaderIQ is a site I frequent. They list free and discounted books, but what I really like is that once you sign up (just an email address), you can track books or authors and once a book you're tracking (or any books by an author you're tracking) falls below a certain price point you set (or a certain percentage you set), you'll receive an email with a link to the book, so you can purchase it at the discounted price.
And, of course, if your library subscribes to Hoopla or Overdrive, you can borrow books for free just as you would any print library book.
I'm sure that some people will find it strange that an author would be promoting free or discounted books, but I feel that books should be available to all of us, I know that not everyone can afford to buy books at full price (especially now), and I trust that most readers who are able will continue to support their favorite authors so that they can pay their bills and continue writing wonderful books.
I hope this has been helpful. Enjoy and Happy Reading!