Physics Textbook Recommendations

Physics (also known as "natural philosophy") is the analysis of nature that is conducted in order to model phenomena to describe how the universe behaves and gain partial understanding of it. One must keep in mind that physical laws and theories are never proven nor refuted but examined on how well they are in agreement to observations and in what domain of physical parameters (speed, temperature, pressure, field strength, etc) they remain in acceptable agreement with experimental observations. While it may be very tempting to assume our equations are the unbreakable rules or source code of the universe, we must realize that such absolute knowledge is fundamentally and hopelessly unknowable.

High School

High school/Freshman physics is a broad survey of the fundamentals of physics: Kinematics and Mechanics, Waves and Acoustics, Thermodynamics, Electricity and Magnetism, Optics and Light, Special Relativity, and Quantum Mechanics which may or may not be done in that order and may have a brief superficial discussion of further topics like Solid-State, Nuclear, or Particle Physics. The mathematical prerequisite is just Precalculus/Trigonometry but with the assumption you are at least taking the Calculus sequence at the same time as a co-requisite and topics from calculus will steadily appear as you progress. Of course, already knowing some calculus ahead of time will be an added benefit.

These are 3 gold standard textbooks

Young and Freedman - University Physics with Modern Physics
Halliday - Fundamentals of Physics
Serway - Physics for Scientists and Engineers

The following are "honors" level alternatives to the above tomes but they don't quite cover everything (such as fluids and other small topics) so be aware to supplement them if you insist on studying out of them. Alternatively, you can use them for additional practice and insight with the above text (but don't feel obligated to read them before moving on to undergraduate level books). The level of required math is a bit higher and assumes you already know calculus.

Kleppner & Kolenkow - An Introduction to Mechanics
Purcell & Morin - Electricity and Magnetism
Georgi - The Physics of Waves
Fermi - Thermodynamics (Dover Books on Physics)
Eisberg & Resnick - Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles

Undergraduate

The essential mathematical prerequisites are Vector Calculus, Matrix Algebra, and Ordinary Differential Equations. You're also assumed to be concurrently learning Partial Differential Equations, Probability, Fourier Transforms, Complex Variables, Special Functions, and Calculus of Variations as you progress. Most books will tend to have some brief introductory remarks on them when needed but it will only cover just enough material to solve the chapter's problems and are really designed to serve as motivation to go out and fully learn them. The more math you know in advance, the clearer the material will be.

Beyond these topics, physics majors are expected to take a number of labs and seminar courses covering Error Analysis, Electronics and Instrumentation, Scientific Integrity (You might think it's unlikely but fraud in physics research does happen. The most famous example being Jan Hendrik Schön who was once thought to be on his way to the Nobel Prize in Physics with completely fraudulent fabricated research), and Experimental Modern Physics.

Sooner or later, physics majors pick up a computer algebra system like Maple, MuPAD (Matlab's Symbolic Math Toolbox), Mathematica, or Python + SymPy to help symbolically solve tricky problems. Similarly, depending on what field and research they pursue, they also learn programming in C++, Fortran, Matlab, Python, IDL and/or LabVIEW as well as others. If you're aiming to get familiar with programming before you need it, it's recommended to start with C++ and learning data structures. While data structures aren't often used for computational physics work, they make excellent subject matter for practice material.

Supplemental Reading

Feynman - Lectures on Physics (Supplement for insight into physics)
Joos - Theoretical Physics (Dover Books on Physics)

Classical Mechanics

Taylor - Classical Mechanics (Great for self study and contains a nice chapter on SR)
Gregory - Classical Mechanics (More to the point than Taylor)
Woodhouse - Introduction to Analytical Dynamics (Mathematical oriented complement to the above)
Sussman and Wisdom - Structure and Interpretation of Classical Mechanics
- Sussman has also authored the classical computer science text, Structure and Interpretation of Computer Programs. The book takes an idiosyncratic approach to classical mechanics that uses the functional programming language Scheme to program various equations, and asks students to do the same, as a conceptual aid to eliminate ambiguity from traditional mathematical notation. The book is freely available here in HTML format. Related materials may be found here.

Special Relativity

Taylor and Wheeler - Spacetime Physics: Introduction to Special Relativity (Low level but good for conceptual understanding)
Woodhouse - Special Relativity (Nice brisk mathematical treatment of SR. See also Woodhouse's General Relativity book for a continuation)
Wolfgang Rindler - Introduction to Special Relativity

Electrodynamics

Griffiths - Introduction to Electrodynamics^[Errata] (The standard at most universities)
Wangsness - Electromagnetic Fields (an alternative to Griffiths and a good transition to Jackson)
Shadowitz - The Electromagnetic Field (Dover Books on Physics) (A cheap alternative and/or supplement to Griffiths, it does electricity and magnetism side by side rather than segregating them)
Schwartz - Principles of Electrodynamics (Dover Books on Physics) (Another cheap supplement to Griffiths, it's a tad more advanced and mathematical and with an emphasis on SR.)

For more on applications when you're done, see EEE's Electromagnetics recommendations.

Thermal Physics

The books on Thermal Physics aren't as great as you would hope they be. If you have the time, try to work through an Engineering Thermodynamics textbook to build up your familiarity with the subject matter before attempting to dive into the theory.

Schroeder - An Introduction to Thermal Physics ^[Site]
Kittel and Kroemer - Thermal Physics
Reif - Fundamentals of Statistical and Thermal Physics
Blundell & Blundell - Concepts in Thermal Physics^[Errata]

A short and insightful supplement or second pass on thermodynamics is Pippard's "Elements of Classical Thermodynamics". For deeper historical and conceptual understanding, check out some the writings of the creators of the subject like Maxwell, Botzmann, Ehrenfest, and Planck on the History page.

Quantum Mechanics

Griffiths - Introduction to Quantum Mechanics^[Errata] (better for students with little exposure to QM)
Townsend - A Modern Approach to Quantum Mechanics (undergrad version of Sakurai)
Shankar - Principles of Quantum Mechanics (better for students with stronger preparation)

Additionally, the following books take a more conceptual and foundational approach rather than problem solving focus the above have.

Schumacher and Westmoreland - Quantum Processes, Systems, and Information
David Bohm - Quantum Theory (Dover Books on Physics) (Sadly no Bohmian Mechanics, does a great job linking the development of quantum mechanics from classical mechanics)
Peres - Quantum Theory: Concepts and Methods

And for philosophy of QM (by physicists who know what the fuck they're talking about):

Bell - Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy
Max Jammer - The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective

Problem Books in QM

Galitski, Karnakov, Kogan, and Galitski Jr - Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers (Expanded version of Problems in Quantum Mechanics (Dover Books on Physics) by Kogan and Galitskiy)
ter Haar - Problems in Quantum Mechanics (Dover Books on Physics)
Squires - Problems in Quantum Mechanics: With Solutions
Tamvakis - Problems and Solutions in Quantum Mechanics

Special Topics

Optics

Fowles - Introduction to Modern Optics (Dover Books on Physics)

Unfortunately this is pretty much the only good book on Optics at this level, the standard books at most universities are Hecht's "Optics" and Pedrotti, Pedrotti & Pedrotti's "Introduction to Optics", both of these books are severely flawed and would be impossible to use for self-study.

For more information on optics, see EEE's Photonics and Optics recommendations.

Fluid Mechanics

Acheson - Elementary Fluid Dynamics
Batchelor - An Introduction to Fluid Dynamics

Acoustics

Kinsler - Fundamentals of Acoustics

Solid State

Simon - The Oxford Solid State Basics (2013) ^{[Online lectures by the author, Site]}
Harrison - Solid State Theory (1970) (Dover Books on Physics)
Kittel - Introduction to solid state physics (2005)
Ashcroft & Mermin - Solid State Physics (1976)
Ziman - Principles of the Theory of Solids (1979)
Mihály & Martin - Solid State Physics: Problems and Solutions (Supplement)

For more information on semiconductors, see EEE's Semiconductor Device Physics recommendations.

Atomic Physics

Foot - Atomic Physics
Bransden and Joachain - Physics of Atoms and Molecules
Haken and Wolf - The Physics of Atoms and Quanta: Introduction to Experiments and Theory

Nuclear Physics

Krane - Introductory Nuclear Physics
Walecka - Theoretical Nuclear & Subnuclear Physics

Particle Physics

Griffiths - Introduction to Elementary Particles^[Errata]
Thomson - Modern Particle Physics
Martin & Halzen - Quarks & Leptons

Astrophysics

Carroll and Ostlie - An Introduction to Modern Astrophysics
Ryden - Introduction to Cosmology
Choudhuri - Astrophysics for Physicists

See the Astronomy Textbook Recommendations for more advanced material on astrophysics.

Relativity

Schutz - A First Course in General Relativity
Kolecki/NASA - Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity
Woodhouse - General Relativity (A continuation of his Special Relativity book, also mathematically brisk)

See also the Astronomy General Relativity recommendations

Graduate

Required Reading

Landau & Lifshitz - Course of Theoretical Physics Volumes 1-10:
1. Mechanics (Covers classical mechanics without special or general relativity, in the Lagrangian and Hamiltonian formalisms)
2. The Classical Theory of Fields (Covers relativistic mechanics of particles and classical field theory; specifically special relativity and electromagnetism, general relativity and gravitation)
3. Quantum Mechanics: Non-Relativistic Theory
4. Quantum Electrodynamics
5. Statistical Physics, Part 1 (Covers general statistical mechanics and thermodynamics and applications, including chemical reactions, phase transitions, and condensed matter physics)
6. Fluid Mechanics
7. Theory of Elasticity
8. Electrodynamics of Continuous Media
9. Statistical Physics, Part 2: Theory of the Condensed State
10. Physical Kinetics
Pauli Lectures on Physics: Volumes 1-6 (Dover Books on Physics)
1. Electrodynamics
2. Optics and the Theory of Electrons
3. Thermodynamics and the Kinetic Theory of Gases
4. Statistical Mechanics
5. Wave Mechanics
6. Selected Topics in Field Quantization
Sommerfeld - Lectures on Theoretical Physics: Volumes 1-6 (Oldie and lesser known but still deserves love)
1. Mechanics
2. Mechanics of Deformable Bodies
3. Electrodynamics
4. Optics
5. Thermodynamics and Statistical Mechanics
6. Partial Differential Equations in Physics

Analytical Mechanics

Goldstein - Classical Mechanics^{[Errata and Bibliography]}
Scheck - Mechanics
Corben and Stehle - Classical Mechanics (Dover Books on Physics)
Arnold - Mathematical Methods of Classical Mechanics
Abraham and Marsden - Foundations of Mechanics (very advanced)
Whittaker - A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Classic reference)

Classical Electrodynamics

Jackson - Classical Electrodynamics (Required hazing - no exceptions)
Panofsky and Phillips - Classical Electricity and Magnetism (Dover Books on Physics)
Smythe - Static And Dynamic Electricity (Harder than Jackson)
Schwinger - Classical Electrodynamics
Zangwill - Modern Electrodynamics
Scheck - Classical Field Theory

Statistical Mechanics

Reichl - A Modern Course in Statistical Physics
Pathria and Beale - Statistical Mechanics
Kardar - Statistical Physics of Particles

SM2: Statistical Field Theory

Kardar - Statistical Physics of Fields
Mussardo - Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics
Giorgio Parisi - Statistical Field Theory

Computational Statistical Mechanics

Tuckerman - Statistical Mechanics: Theory and Molecular Simulation
Krauth - Statistical Mechanics: Algorithms and Computations

Quantum Theory

Sakurai - Modern Quantum Mechanics
Sakurai - Advanced Quantum Mechanics (dated but useful to bridge QM to QFT)
Gottfried and Yan - Quantum Mechanics: Fundamentals^[Errata] (Modern, rigorous, and complete)

2 more idiosyncratic books:

Ballentine - Quantum Mechanics: A Modern Development (Uses the Ensemble interpretation rather than the Copenhagen interpretation)
Weinberg - Lectures on Quantum Mechanics

QM References

Messiah - Quantum Mechanics (Dover Books on Physics)
Dirac - The Principles Of Quantum Mechanics (Classic)
Cohen-Tannoudji, Diu, and Laloë - Quantum Mechanics: Volumes 1&2
Schwinger - Quantum Mechanics: Symbolism of Atomic Measurements (An unique and different perspective on QM)

For culture and insight, see some of the influential papers on Quantum Theory on the History page

Path Integrals

Feynman, Hibbs, and Styer - Quantum Mechanics and Path Integrals: Emended Edition (Dover Books on Physics)
Schulman - Techniques and Applications of Path Integration (Dover Books on Physics)
Kleinert - Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

Quantum Field Theories

Peskin & Schroeder - An Introduction to Quantum Field Theory ^[Errata]
Schwartz - Quantum Field Theory and the Standard Model ^[Errata]
Srednicki - Quantum Field Theory ^{[Draft and errata]}
Weinberg - The Quantum Theory of Fields
Ryder - Quantum Field Theory
Itzykson & Zuber - Quantum Field Theory

Many-Body Physics

Fetter and Walecka - Quantum Theory of Many-Particle Systems (Dover Books on Physics)
Negele and Orland - Quantum Many-particle Systems
Mahan - Many-Particle Physics
Coleman - Introduction to Many-Body Physics
Altland and Simons - Condensed Matter Field Theory

General Relativity

Schutz - Geometrical Methods of Mathematical Physics
Wald - General Relativity
Misner, Thorne, & Wheeler - Gravitation
Lightman, Press, Price, & Teukolsky - Problem Book in Relativity and Gravitation (supplement)

Mathematics Resources

Hassani - Mathematical Physics: A Modern Introduction to Its Foundations
Szekeres - A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry
Nakahara - Geometry, Topology and Physics
Frankel - The Geometry of Physics
Reed & Simon - Methods of Modern Mathematical Physics I: Functional Analysis; II: Fourier Analysis, Self-Adjointness; III: Scattering Theory; IV: Analysis of Operators

Quantum Field Theory in Curved Spacetime

Mukhanov and Winitzki - Introduction to Quantum Effects in Gravity
Birrell and Davies - Quantum Fields in Curved Space
Parker and Toms - Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity

String Theory

Becker, Becker, and Schwarz - String Theory and M-Theory: A Modern Introduction
Polchinski - String Theory, Volume I: An Introduction to the Bosonic String; II: Superstring Theory and Beyond
Zwiebach - A First Course in String Theory (Approachable by an advanced undergraduate)
Green, Schwarz and Witten - Superstring Theory