Griffiths, D.J., Introduction to Quantum Mechanics
Cohen-Tannoudji, C., Dui, B., & Laloe, F., Quantum Mechanics
[J.W.] This book really has it all. It comes in two huge volumes, sold separately at about $90 each, so for the price it should. It's a very complete, generally well-thought out portrait of quantum in all its glory. The downside is that, if you're learning quantum for the first time, there's a lot of stuff to slog through that you may not care about, and it can be hard to decide what to read and what not to read. But if you already know quantum, it makes a fantastic reference as it's clear and hyper-complete. C-T. is sometimess criticized for the complex chapter/supplement/exercise organization, but really, if you can't figure out how the chapters work, what are you doing reading about quantum mechanics?
Shankar, R., Principles of Quantum Mechanics
Shankar is a good modern introduction to quantum mechanics. It begins with a very long chapter (~80 pages) on the necessary mathematics, i.e. linear algebra & linear operators. Then it lays down the postulates of quantum physics, and goes on to a talkly, reasonably thorough study of the basic applications of quantum mechanics. It's not complete, but it doesn't pretend to be. I have two complaints: The problems are often "canned"--that is, they are easily solvable, and not so closely related to the real world. Second, the quality of the problems--their individual completeness and relevance to the text--takes a downhill turn around chapter 12.
[J.W.] More chatty than Cohen-Tannoudji, but less complete (and cheaper), Shankar is a good book from which to initially learn quantum. Once you already know the subject, you'll probably find yourself frusterated or annoyed by its sometimes superficial treatments and its general lack of sophistication, but once you've reached this point, the book isn't really meant for you anyways. Again, a good introduction.
Townsend, J.S., A Modern Approach to Quantum Mechanics
I can't point to any particular reasons that I like this book, but I do indeed like it. It's a well thought-out coherent study of the structure and essential techniques of quantum mechanics...very nice for a second reading on quantum theory. It's reads like a kind of undergraduate Sakurai, but it's got strengths that Sakurai doesn't. (For one thing, Townsend did not die midway through writing his book.) It's a little less cavalier in its derivations, and a little more careful in its expositions. I guess that's because it was intended as an undergraduate text.
Edmonds, A.R., Angular Momentum in Quantum Mechanics
My little reference on the quantum theory of angular momentum. Edmonds has efficient derivations of all of the essential theory: irreducible representations of the rotation group, spherical harmonics, Clebsh-Gordon coefficients, Wigner-Eckhardt theorem,etc,... Next to no applications and no problems, but it's come in very handy from time to time. There's usually a copy at Powell's for $6.
Dirac, P.A.M., The Principles of Quantum Mechanics
The classic exposition of quantum mechanics, written by the first person to really understand the theory, Dirac's book is usually put on the same shelf as Newton's Principia. It is still worth reading today, because it's filled with amazing insights into the structure of quantum theory. It's a distinct pleasure, to see that Dirac pays attention to all of the physical subtleties which are glossed over in more recent textbooks.
I sometimes tell people that a theoretical physicist's reputation depends on how long it takes mathematicians to turn his half-assed ideas into rigorous mathematics. It took more than a decade for mathematicians to make sense of the delta "function," and much longer than that for them to understand his bra-ket formalism. In fact, it was never really understood in one sense: It's still very easy to get non-sensical results from the formalism by pushing it in the wrong direction.
Feynman, R.P. & Hibbs, A., Quantum Mechanics and Path Integrals
Feynman must have been a greater theorist than Dirac, because no mathematician yet has really made sense of his path integral formalism. (See the review of Dirac's book above.) Nonetheless, Feynman's book is a worthwhile read. It's still the nicest exposition of the subject I've seen, packed with typical Feynman insights. Besides, it's worth reading just to see what Feynman had in mind. (His notion of defining path integrals as suitably regularized limits of normal integrals is essentially the only way of dealing with the damned things in anything resembly a rigorous manner.)
Schiff, L., Quantum Mechanics
I've been told that (a) Schiff's book is really just a transcription of Oppenheimer's Berkeley lectures on quantum theory, updated at suitable points, and (b) that it's rife with errors and typos. I don't know about the truth of either of these, because I've never used Schiff as anything but a reference. It's a pretty complete coverage, and despite an occaionally annoying typeset, it's good for looking things up.
Landau, L.D., A Course of Theoretical Physics, Vol. III: Quantum Mechanics
Typical Landau: efficient, elegant exposition of the subject, packed with brilliant insights and covering topics you absolutely will not find elsewhere. In particular, Landau's discussion of the measurement processs in terms of wave functions may be the single most amazing piece of physics I've ever seen. The problems are also particularly good in this one, and the special functions appendix is extremely useful.
Sakurai, J.J, Modern Quantum Mechanics
A popular graduate text, Sakurai's book really does live up to its title: It uses symmetry as an organizing principle, and this is the hallmark of modern physics. The text is, for the most part, well-written, and it contains a host of good problems. Mathematics is sometimes given short-shrift here--hard to avoid in a text for a general physics audience--but the physical reasoning usually makes up for it. Unfortunately, Sakurai died before completing his book, and the later chapters are not as good as the early ones.
Merzbacher, E., Quantum Mechanics
Another popular graduate text, Merzbacher is not as modern as Sakurai in its emphasis, but it covers a much broader range of topics. Sakurai's book is better for the basic principles, but Merzbacher's is better for things like scattering theory and approximation techniques and all of their various applications.