The American Mathematical Society maintains a page with links to Reviews of Books, Plays, and Films related to mathematics. The emphasis is on books and reviews accessible to a broad audience.
The Notices of the AMS runs one or two reviews per issue; links to past reviews from theNotices can be found on the page above.
The Bulletin of the AMS runs detailed reviews of more technical books.
SIAM News runs a couple of book reviews per issue.
MAA FOCUS has an “On Books” column that reprints selected MAA Reviews.
MathSciNet is the online version of Mathematical Reviews. The main focus is on research papers, of course, but many books are also reviewed.
The American Mathematical Monthly runs one or two longer reviews per issue.
Mathematics Magazine and The College Mathematics Journal also publish reviews, though not as regularly as the Monthly. The CMJ includes a “Media Highlights” column that includes brief comments on books, articles, and other appearances of mathematics in the media.
Math Horizons runs regular book reviews, usually written by undergraduates.
SIAM Review runs many book reviews in each of its issues.
Know other good online sources? Email the editor: fqgouvea at Colby dot edu.