Your public library
I know it isn't what some new bloggers want to hear, but many sources of review copies only want to use established bloggers. Review your favorite books regularly; eventually you will be established.
The Catholic Company
The Catholic Company is a Catholic bookstore which allows most Catholic bloggers to join its review program. They publish a list of books on which they want reviews. As a blogger, you are allowed to order one at a time, as many as you are able to read and review. Right now there are thirty-three items on their list ranging from prayer books to biographies. They rarely have fiction but there are exceptions (like the Lily books I've reviewed). Join here.
Tiber River Reviewers
The Tiber River Review program is run by Aquinas and More Catholic Bookstore. You can join here. The program is similar to The Catholic Company's but they limit the number of free books you can obtain per year. However, they encourage you to post reviews of other Catholic books you purchase or otherwise obtain, rewarding you with points which can eventually be traded for books or other merchandise. While they have some good material, I find their site difficult to use and I often don't receive books I thought I was requesting.
Booksneeze is the program of Thomas Nelson publishers. At this moment they have a large number of digital review copies available, both fiction and non-fiction. They also have children's books. The print books they have right now deal mainly with spiritual growth and development. Booksneeze is very popular and if you want print copies, you need to keep a close eye on their site and grab them when they go up. Many of the same digital books available on their site are available via NetGalley. Join here.
Tyndale Blog Network
You can join the Tyndale Blog Network here. It is run by Tyndale, a Christian publisher. As with other programs, available books are posted on their website and you are obligated to review those you receive.
Blogging for Books
Waterbrook Multnomah's program is called Blogging for Books and you can join here. Like the others, you review a list of offered books, request what you want, and then post a review. They offer both print and digital books.
First Wilcard is a blog tour group that tours Christian fiction. To join, you have to have been blogging for at least six months, post at least once a week and have an established readership. It operates via a yahoogroup. Members are sent emails offering books and reply to request those desired. Requesting a book does not obligate you to post a review, only the tour material, which is posted on the group blog a couple of days before the tour day. Reviews are encouraged however.
Book Blogs Ning
Book Blogs Ning is a group of message boards on which review copies are often offered. Surf around, join groups that interest you and see what happens.
Net Galley provides digital galleys to "professional readers", including bloggers. Galleys for Kindles are permanently yours after download; those for readers using Adobe Digital Editions (such as the Nook) expire 90 days after download. Right now NetGalley has over 2200 books available from cookbooks to children's books, from devotionals to erotica. When you register you are asked to submit information about your blog and reading preferences. When you request a title, the publisher uses that information to decide whether or not to grant you access. Some publishers automatically approve everyone; others put some bloggers on auto-approve and personally approve or disapprove others. While I am no heavy hitter in the book blogging world, I find far more books on NetGalley than I could ever read. While you are not obligated to review books you download, publishers are able to determine how many books you download and how many you review, so my guess is that if you always download and never review, you'll find your access diminished.
Like NetGalley, edelweiss is a source of digital galleys. It is also a source for publisher's catalogs so you see a full list of all upcoming books from that publisher, which may allow you to send a request for a review copy directly to the publisher. Again, that works better if you have a substantial readership.