Update (05/15/16): tl;dr: I would give this book more stars if it is titled "Introduction to Wave Mechanics."
First, the good: this book doesn't requirUpdate (05/15/16): tl;dr: I would give this book more stars if it is titled "Introduction to Wave Mechanics."
First, the good: this book doesn't require mastery of "advanced" classical physics and math such as Lagrangian and Hamiltonian mechanics, electromagnetism, partial differential equations, linear algebra, or statistics. For example, Griffiths takes his time to explain standard deviations, separation of variables, and phase and group velocity in the beginning. This makes the book very accessible.
The bad: While a step by step calculation makes it easy to follow, one often gets lost in details and misses the big picture. This is not helped by the fact that the book shies away from the math of QM: linear algebra and the concise Dirac notation, which is introduced but quickly discarded.
The author takes the shut-up-and-calculate approach to the extreme (like how standard freshman physics textbooks present QM). The formalism is not developed logically, and, overall, the book is very weak in formalism. For example, the Schrödinger equation specialized to the position space is given from the get-go with the motivation that it is the quantum equivalence of Newton's equation of motion, which is true, but not really helpful; a child may be familiar with the notion of forces, but not Hamiltonians and complex amplitudes. The many subtleties of postulates are never spelled out. (Compare this to e.g. chapter 4 of Shankar's Principles of Quantum Mechanics (Hardcover))
An important fact that quantum states (and not wave functions) and operators in Hilbert space are geometric objects that do not depend on a particular representation is not emphasized enough; when discussing finite-dimensional systems, Griffiths never demonstrates a change of (orthonormal) basis. Symmetry and change-of-basis transformations only make a brief appearance as 2 and 3-star end-chapter problems (which, according to the author's rating scheme, are difficult or peripheral problems) and even there he still doesn't tell you that they are unitary matrices!
The use of the word spinors interchangeably with two-element column matrices does not help in the slightest. Two-element column matrices are two-element column matrices. Spinors are related to representations of rotation groups, to which Griffiths makes no connection.
He also makes degenerate perturbation theory looks complicate, whereas in fact it is just diagonalizing the degenerated submatrix.
In conclusion, it seems that everything involving matrices is so badly treated that this book should be called Introduction to Wave Mechanics.
I used this book for an undergraduate course taught by an excellent professor. (He made up all the problem sets. So I can't judge the quality of problems in Griffiths.) And I had learned Dirac notation by myself beforehand (from Sakurai's Modern Quantum Mechanics). I can recommend it to an absolute beginner, but with the caveat that this cannot be your last QM book if you want to understand QM. Griffiths prepares you in wave mechanics for e.g. spectroscopy and scattering calculations, but for the foundations of QM, look elsewhere. (A very nice second book explicitly aiming to clear up the conceptual understanding of those who just finish this kind of "wave mechanics" course is Isham's Lectures on Quantum Theory: Mathematical and Structural Foundations.)