Here is a list of many of the review programs I use to get my books. Some of them require a min amount of followers, so keep that in mind. As well that some of these programs have time limits for you to write reviews. (A majority of these publishers or programs are Christian)
Tyndale Blog Network. Part of Tyndale Publishing, a Christian publisher, Tyndale Blog Network has a great selection of books like nonfiction, devotionals, fiction, adventure, etc, for you to review and you can now review up to 2 books! (just started in 2014) They send you email you as soon as they release the new monthly choices, and their facebook group will sometimes have giveaways.
Blogging For Books. Although Blogging For Books used to be completely Christian, (Waterbrook Publishers) it has now joined up with many other publishers. You choose each book in a section such as Fiction, Faith, Cooking, Non-fiction, etc. They'll give you a list of publishers and you can choose which books you want. I definitely suggest using this, as Waterbrook offers some excellent books to read.
MP Newsroom, a division of Moody Publishers, offers a wide variety of books from kids books to biographies. You can review up to 2 books at a time.
Revell is a division of Baker Publishing. They send out 2 monthly emails (one fiction, the other nonfiction) of different books to review.
Bethany House, another division of Baker Publishing Group, sends out 2 monthly newsletters. Though this doesn't guarantee you will receive the book.
Baker Books sends 2 monthly newsletters, and is connected to a few other publishing groups.
They offer a great opportunities like author interviews, giveaways, and more. They also require 800 unique page-views a month.
BookLookBloggers requires 30 followers, and is the combined companies of Thomas Nelson and Harper Collins.
You can click the pictures to go to each company, or search for each publishing group.
This is not a list of all blogging companies. If you have any blogging websites that you know of comment below with the website and I'll be happy to add it in the list.