BookDaily allows you to read the entire first chapter of any of the over 60,000 titles in it's database. They have a very user-friendly search system where you can search by title, genre, author, etc. Yes, this site includes newly released and bestseller books.
You can fill out a brief profile listing your interests and elect to receive an email from them 3 times per week or a "Featured Book of the Day" email or both. Under 'subscriptions' on your profile, you can also receive a daily sample based on a category (e.g., romance, mystery, sci/fi) or a weekly update by genre (lots of choices here, too). Because I read a lot of nonfiction, I really appreciate that BookDaily has so many nonfiction books on their site. You're also provided with what's called 'My Sample Shelf' where you can put books that you're interested in but don't have time to read the chapters as you come across the books. That way they're waiting for you on your 'shelf' for when you do have time to read.
A shout out to my old friend, Becky, for 'accidentally' causing me to think of posting about this site!
At Iambik Audiobooks we also have the entire first chapter available for listening for all of our books. Unlike the big store sites where our books are also for sale, like Amazon and Audible, our clips aren't simply taken from some part of the book, you get the whole banana. We know that often it's the first chapter that can hook a reader so drop by and give us a listen.