Landau and Lifshitz: Classical Mechanics
Excellent Text. Brief and to the point. They do not derive the Hamilton Jacobi Equation in terms of vector fields though. A mistake, in my opinion.
Goldtein: Classical Mechanics
More worked out examples than Landau, but with the same deficiency with regard to the HJE.
Giffiths: Quantum Mechanics
An Excellent Introduction for learning how to solve the Schrodinger Equation. Like most other QM texts though, the interpretation is unsatisfying, to put it mildly. The S.E. is simply brought into existence, out of thin air. The connection with Classical Mechanics is obscure. Measurement is never defined in terms of more basic concepts.
Bohm and Hiley: The Undivided Universe
Contains a much better attempt at explaining Quantum Theory than the standard approach, in my opinion (though it does have issues).
A great overview of decoherence.
Multiple Authors: Many Worlds?
Probably my favorite QM book right now. Not for beginners though.
David Deutsch: The Fabric of Reality
An unapologetic endorsement (though not a technical description) of the Many-Worlds approach.
Kim Joris Boström: Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics
Presents essentially the same idea as this blog. The approach is different and in many ways complementary though. Highly recommended.
All calculations, images, and animations were created with Mathematica 7.0.