This question attempts to collect the few pearls among the dozens of bad C++ books that are published every year.
Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book. It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles.
Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in the C++ chat roomthe C++ chat room. (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list. Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review.