This introductory text by Griffiths has two major advantages: first it is exceedingly interesting to read, at such an extent one could believe the material is easy. Exercises are challenging enough to show it is just an impression. Second, the text covers a rather big amount of the (non-relativistic) theory, in a concision which is exemplar. It is a short text, which travels in the corners of the field: quantum statistics, solid state physics, perturbation theories, scattering... Of course the counterpart is those topics aren't dealt with at depth. This is a book to see things, before to work on them. For all those reasons, it is a very, very bad reference, but it is not its purpose. For example, the bra and ket formalism is introduced a bit lately, and its use is not stressed. The functional notation for what is currently referred to as |n, l, m> conceals the power of Dirac notations. Tensor product of Hilbert space are completely omitted, thus obscuring the (short but important) section on angular momenta, especially their addition. However, following the book's spirit, you have an opportunity to see Clebsch-Gordan coefficients at work, with their pretty cascading tables.
The book is accessible without serious prerequisites, not even in electromagnetism, you just need to know the basis of calculus. Therefore it is the text to get if as a beginner you want to get acquainted with this fundamental piece of physics, along with learning your first physical theories (mechanics or electromagnetism). For others, it is useless to they who ever know pretty much of the theory, even as a review. To students who encounter this strange world for the first time, but with a fierce amount of classical knowledge on their back, I recommend it either as a companion to a more demanding detailed text--Shankar seeming the perfect pick--or as the only text if tremendous amount of personal work is to be furnished to fill in and explore by oneself what is missing. I wouldn't rely too much on it however.