Let me list the books on various topics in physics which I find the best in their fields:
1) Arnold "Mathematical Methods of Classical Mechanics" (contains a beautiful intro into various mathematical topics -- symplectic geometry, contact geometry, differential forms, Lie groups, etc. -- and their applications in Hamiltonian and Lagrangian formalisms of mechanics);
2) Schwinger "Classical Electrodynamics" (standard course in EM in vacuum and media, but given from more modern viewpoint and describes relatively advanced techniques, such as Green's functions);
3) Rubakov "Classical Theory of Fields" (an excellent course for undergraduates, introducing many advanced topics -- solitons, instantons, monopoles, non-commutative fields theories, index theorems -- but requires only knowledge of classical mechanics and electrodynamics);
4) Shankar "Principles of Quantum Mechanics" (as for me, the best book on QM, introducing it from quite a formal point of view. Contains all the standard material + Feynman Integral for bosons and fermions, density matrix, etc. The only shortcoming is easy problems). May be supplemented by some good book of problems, such as "Exploring Quantum Mechanics: a Collection of 700+ Problems for Students, Lecturers and Researchers" by Galitski and Karnakov;
5) Carroll "Spacetime and Geometry: an Introduction to General Relativity" (good book presenting GR from a modern geometrical point of view. Moreover, contains some modern topics -- Hawking Radiation, Unruh Effect, etc). "General Relativity" by Wald and "Gravitation" by Misner, Thorne and Wheeler are also good, but I don't think one should begin studying the subject with them. There is also a very good problem book on GR -- "Problem Book in Relativity and Gravitation" by Lightman, Press, Price and Teukolsky.
6) Nakahara "Geometry, Topology and Physics" (contains basically all the math needed to study GR, QFT and String Theory);
7) Srednicki "Quantum Field Theory" (my favorite textbook on QFT, containing introduction to all the essential topics in QFT. Can be supplemented by some more advanced textbooks, such as Weinberg's "The Quantum Theory of Fields");
8) Green, Schwarz, Witten "Superstring Theory" (a classical reference on String Theory. Doesn't discuss any modern topic, but the material it contains covered wonderfully. May be read in parallel with Polchinski's "String Theory"). The best place to study more modern topics in the field is "D-branes" by Johnson, as for me.