Many of the specialized subject specific online indexes include book reviews. These are some of the broader subject specific indexes with book reviews.
These indexes cover publications in all subject areas and are good sources for recent book reviews. Make sure the indexes cover the date of your book's publication! All have some, but not complete, full text.
Book Review Digest, 1905 to date.
Z 1219 .C96 West Reference
In print only with citations and brief excerpts from reviews only. No full text.
There are thousands of Web sites that provide book reviews. This is a selected list of some of my favorites.