Although the article and report tags exist, it seems that whenever the books tag was incorrectly applied to a question about the book class, the tag was removed, but nobody bothered to create a separate book tag. My guess is that such a tag (like article and report) would "only" reveal what should be revealed by a MWE, namely, the class used by the questioner. Any special expertise needed for questions about book is most likely also useful for report, and more often than not useful for article. The AMS classes sometimes deviate from the standard classes, but again there are similiarities between amsart and amsbook (there's no amsreprt class).
Another hint that those four tags were ill-conceived is that each of them has at most 2 followers -- compare that to the 35 followers of memoir and the 31 of koma-script, both of them popular classes.
I suggest to not create a separate book tag. Instead,
EDIT: Judging from the upvotes and comments, the consensus seems to be that the class-specific tags should be abandoned and generic tags standard-classes and ams-classes should be created. However, on second thought I share Jubob's concern that standard-classes is likely to be overused, so I suggest to restrict the use of this tag to the "inner workings" of the standard classes (similar to the latex-kernel tag). The tag wiki excerpts could read as follows:
{standard-classes} is about the inner workings of the standard classes
article, book, and report. Do not add this tag simply because
you use one of these classes; instead, choose the tags appropriate for
your specific problem.
{ams-classes} is about the AMS classes amsart, amsbook, and
amsproc. When using this tag, add the tags appropriate for your
specific problem.
Following this definition, it is likely that some of the questions featuring article or report at the moment should simply have these tags removed instead of replaced by standard-classes. I will check these questions in the next days.
