I think there are some excellent recommendations above. I learned quantum mechanics for real from Shankar, I think it's a great choice. Griffiths is also a great physics text. I would also recommend these following less famous books:
Physical chemistry and materials science textbooks. I would also highly recommend newer textbooks in physical chemistry as a perhaps less obvious place to look for excellent introductions to quantum mechanics - as Dirac famously said once, it's really the foundation for all of chemistry. An excellent physical chemistry is Physical Chemistry by Berry, Rice and Ross. Presumably there are also good introductions in materials science books, although I don't have any to recommend.
Not Feynman. In my opinion Feynman's Lectures in Physics is great for insight, but it's a terrible idea to learn anything from it the first time - remember that when Feynman actually lectured, most of the freshmen and sophomores (the intended audience) dropped the course, and were replaced by senior students!
Weyl (group theory). I'm surprised no one's mentioned Hermann Weyl's textbook "Theory of groups and quantum mechanics". It's an oldie but goodie, and perhaps best appreciated with someone with a good background in group theory.
Lieb (analysis). I recommend Elliott Lieb's Analysis GSM textbook - on the surface, it looks like it's about functional analysis, but it's secretly also a text on quantum mechanics!
There are some subjects that none of the introductory quantum mechanics texts I've read ever do a satisfactory job of explaining, and I think are really worth following up after Shankar or another such book. The most important ones I think are:
Many-body phenomena. This is really where some of the strangest predictions of quantum mechanics come from, like the EPR paradox and spin statistics. Levine's Physical Chemistry is an excellent place to start. Another great book is Blaizot and Ripka's Quantum Theory of Finite Systems, which does a superb job with boson and fermion statistics.
Dynamics (time-dependent quantum mechanics. I cannot recommend Tannor's Introduction to Quantum Mechanics: A Time-dependent Perspective enough as a really fantastic resource for learning how practicing physicists and chemists actually do these calculations, beyond the really simplistic calculations presented in most introductory texts. That could also work as a first textbook.
You know, I'm in the building next to you. Maybe you should come by and talk sometime. :)