I've found some nice sources of information and clear explanations during my decade of studying physics. I wish someone had told me about these resources to begin with. This page contains some advice that I would have given myself when I was beginning my college career.
General Recommendations
Schaum's Outlines
Schaum's outlines are an excellent resource for learning the mathematics required for physics majors and graduate students. They are inexpensive, they clearly summarize the material, and they contain many detailed solutions to problems. Many of the books are sufficient to use as a primary source, however the best approach is to have at least one traditional textbook on the subject and one Schaum's Outline if you are teaching yourself. I especially recommend the following:

 Complex Variables
 Advanced Calculus
 Linear Algebra
 Differential Equations
 Partial Differential Equations
 Tensor Calculus
 Fourier Analysis
 Differential Geometry

The Feynman Lectures on Physics
This threevolume set is very rich with clear, concise explanations. It covers practically the entire core physics curriculum including a more thorough discussion of fluid dynamics than most undergraduate physics programs in the United States offer. I highly recommend this to anyone studying physics at the undergraduate or graduate level. Refer to the Wikipedia article for more information:
The Feynman Lectures on Physics.
Landau & Lifshitz Course of Theoretical Physics
This series of ten texts covers the core of graduatelevel physics. Lev Landaulike his American counterpart, Feynmanwas very talented at explaining things.

 vol. 1: Mechanics
 vol. 2: The Classical Theory of Fields
 vol. 3: Quantum Mechanics: NonRelativistic Theory
 vol. 4: Quantum Electrodynamics
 vol. 5: Statistical Physics Pt. 1
 vol. 6: Fluid Mechanics
 vol. 7: Theory of Elasticity
 vol. 8: Electrodynamics of Continuous Media
 vol. 9: Statistical Physics Pt. 2
 vol. 10: Physical Kinetics

Inspiration & Motivation
Studying physics at a university can be arduous and boring at times, so it helps to read some popularizations to remind yourself that physics is fun and exciting once you learn enough. Reading this sort of material can also help you to explain things to people who aren't as interested in physics as you are. Here are a few examples:
Specific Recommendations
Fluid Dynamics
I strongly encourage people to study fluid dynamics because it makes vector and tensor calculus more intuitive. Fluids are found everywhere around us and inside of us, so it's nice to have a good understanding of the general properties of fluid dynamics. Once you understand fluids, you will find that many aspects of electricity & magnetism become intuitive. In addition to volume 2, chapters 39  41 of the Feynman Lectures and volume 6 of Landau & Lifshitz, I recommend the excellent text by Batchelor:
Classical Mechanics
In this case, the standard text by Goldstein already covers the subject very well. If it is supplemented with volume 1 of the Lifshitz & Landau series and volume 2, chapter 19 of the Feynman lectures, you will be likely to have a more solid understanding of the subject. I would recommend studying graduatelevel mechanics after or at the same time that you study tensor calculus.
Electricity & Magnetism / Classical Electrodynamics
As I mentioned above, I recommend studying fluids before electromagnetic theory. In addition to volume 2 of the Feynman Lectures, volumes 2 and 8 of Landau & Lifshitz, and the standard
text by Jackson, I highly recommend:
The text by Jefimenko is very impressive. It contains many clear examples and explanations. The Franklin text contains a nice explanation of shortcuts that can be used when manipulating differental vector operators and it avoids SI units, so it doesn't contain a lot of
's and
's. Thus it's more in line with research papers. The newest edition of Jackson's text uses the SI system in part of the book and then switches to Gaussian units later when it gets to more advanced topics; it's not selfconsistent. The text by Panolfsky and Phillips is a classic that contains a few derivations that are otherwise hard to find; some people consider it the best book on the subject.
Many people are fans of the undergraduate text by
David Griffiths. I can't comment on that particular text since I haven't read it. The text by
Julian Schwinger et al. is probably the most advanced / mathematical graduate text on the subject.
Tensor Calculus
I recommend using a combination of the following books to begin with:
These will introduce you to all of the essential details of the tensor calculus using index notation. They will also provide you with exposure to the two common notations for Christoffel symbols and they include many solved practice problems. To learn more about indexfree notation and applications of tensors, it would probably be best to use a modern general relativity or differential geometry text. For the simplest application, study the stress tensor of fluid dynamics. For an explanation of the difference between covariant and contravariant quantities, I've written
this page.
Quantum Mechanics
Quantum theory is best understood once you have studied the Lagrangian and Hamiltonian formulations of classical mechanics. Having a solid background in the solutions of the partial differential equations appearing in electrostatics is also very helpful. In addition to the third volume of the Feynman Lectures and the third volume of Landau & Lifshitz, one book stands out as being particularly good as a primary text:
It should be supplemented with extra material from other texts, of course. That's always the case. A very interesting and clear introduction to the path integral formulation can be found in
Quantum Mechanics and Path Integrals by Feynman and Hibbs.
Thermodynamics and Statistical Mechanics
In terms of thermodynamics, the book by Fermi provides a very nice introduction to the theory:
I haven't read an exceptional statistical mechanics text yet. A few have a pretty good reputation, so they are on my reading list:
Recommended Order:
As far as I can tell, the best order in which to study graduatelevel physics would be roughly the following. I've organized the material into five phases where the topics in each phase are studied simultaneously:
 mechanics, fluid dynamics and thermodynamics, mathematics (tensor calculus, complex analysis)
 more mechanics, electricity & magnetism, special relativity, more mathematics (PDE's, Green's functions, "special" orthogonal functions)
 more electricity and magnetism (which includes more about special relativity), introductory general relativity, and quantum mechanics
 more quantum mechanics, statistical mechanics, more general relativity, and more mathematics (differential geometry)
 quantum field theory, elementary particles, more statistical mechanics, more mathematics (group theory and topology)
Computational physics and basic computer science can be introduced at any point. I highly recommend that people study probability & statistics, numerical analysis, computational physics, algorithms, data structures, and some basic software engineering in order to be wellrounded.
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I agree that having a solid background in the solutions of the partial differential equations appearing in electrostatics is also very helpful
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Allright studying graduatelevel mechanics after or at the same time that you study tensor calculus
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