Electrical and Electronics Engineering

Introductory Reading and References

Practical Electronics for Inventors by Paul Scherz and Simon Monk (Contains everything you could possibly want to know)
Electronic Devices and Circuit Theory by Boylestad and Nashelsky
Modern Batteries: An Introduction to Electrochemical Power Sources by Vincent and Scrosati (Quick primer on batteries for nonspecialists)
Linden's Handbook of Batteries by Reddy (More up to date and detailed than the above)
Hughes Electrical and Electronic Technology
Standard Handbook for Electrical Engineers

Fundamentals

Background Knowledge

Before you start, you should be familiar with Introductory Physics, and mathematics up to Vector Calculus, Linear Algebra, Ordinary Differential Equations, Complex Variables, Partial Differential Equations, Fourier Transforms, Probability, Stochastic Processes, Statistics, and Special Functions.

Mathematics

Advanced Engineering Mathematics by Erwin Kreyszig
Advanced Engineering Mathematics by Greenberg
Mathematics for Natural Scientists (Vol. 1 & 2) by Lev Kantorovich
Mathematics for Physicists (Dover Books on Physics) by Dennery and Krzywicki

Bible

The Art of Electronics, 3rd edition, Paul Horowitz and Winfield Hill

Circuit Analysis

Electric Circuits by Nilsson and Riedel
Fundamentals of Electric Circuits by Alexander and Sadiku
Foundations of Analog and Digital Electronic Circuits by Agarwal and Lang (Overlaps somewhat with Electronics books)
Linear Circuits by Ronald E. Scott

Get familiar with circuit simulation software like PSPICE, Multisim, LTspice or Tina (best) and use them to check your work.

Electronics

Prerequisite: Circuit Analysis.

Fundamentals of Microelectronics by Razavi
Microelectronic Circuits by Sedra and Smith
Microelectronic Circuit Design by Jaeger and Blalock

Programming

Knowing Matlab and C++/C is essential. Lua or Python can be helpful.

Digital Logic Design and Computer Architecture

See the CS&E recommendations: Computer Architecture and Digital Logic

Probability and Stochastic Processes

The Art Of Probability: For Scientists and Engineers by Hamming (Supplement)
Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers by Yates and Goodman (Very straight forward, a bit too easy)
Introduction to Probability by Bertsekas and Tsitsiklis
Probability in Electrical Engineering & Computer Science: An Application-Driven Course by Walrand (Supplement with various applications)
Probability, Random Variables and Stochastic Processes by Papoulis and Pillai

See also the mathematics page on Probability.

Signals & Systems

Signal Processing and Linear Systems by Lathi
Signals and Systems by Alan V. Oppenheim and Alan S. Willsky
Signal Analysis: Time, Frequency, Scale, and Structure by Allen and Mills ^[Errata]

See the mathematics page on Fourier Transforms for additional material.

Advanced Topics

Digital Signal Processing

Prerequisite: Signals & Systems.

Understanding Digital Signal Processing by Lyons
Digital Signal Processing: A Practical Guide for Engineers and Scientists 1st Edition by Steven Smith (Basic intro, an older version "The Scientist and Engineer's Guide to Digital Signal Processing" is available online)
Introduction to Signal Processing by Sophocles J. Orfanidis (Another good textbook that's freely available online)
Discrete-Time Signal Processing by Alan V. Oppenheim and Ronald W. Schafer (Classic book on DSP) ^{[Online MIT lectures by Oppenheim]}
Digital Signal Processing: Principles, Algorithms and Applications by Proakis and Manolakis (Another classic on par with Oppenheim)

Communication Systems

Prerequisites: Signals & Systems and Probability.

Modern Digital and Analog Communication Systems by Lathi and Ding
Communication Systems by Haykin and Moher
Digital Communications: Fundamentals and Applications by Sklar
Fundamentals of Communication Systems by Proakis and Salehi (Somewhat harder, older editions were called "Communication Systems Engineering")^[Errata]
Digital Communications by Proakis and Salehi (Advanced)

Analog Electronics

Design of Analog CMOS Integrated Circuits by Razavi
CMOS Circuit Design, Layout, and Simulation by Baker
Analysis and Design of Analog Integrated Circuits by Gray, Hurst, Lewis, and Meyer
Analog Integrated Circuit Design by Carusone, Johns, and Martin
Design with Operational Amplifiers and Analog Integrated Circuits by Franco

Power Electronics

Power Electronics: Converters, Applications, and Design by Mohan, Undeland, and Robbins
Fundamentals of Power Electronics by Erickson and Maksimovic
Principles of Power Electronics by Kassakian, Schlecht, and Verghese

Electromagnetics and Transmission Lines

It's helpful to read a book on the physics theory like Griffiths before getting to the applications.

Electromagnetics with Applications by Kraus and Fleisch
Field and Wave Electromagnetics by Cheng
Fundamentals of Applied Electromagnetics by Ulaby, Michielssen, and Ravaioli
Fields and Waves in Communication Electronics by Ramo, Whinnery and Van Duzer
Engineering Electromagnetics by Hayt and Buck (Additional reference)
Electromagnetic Wave Theory by Kong (Advanced)
Advanced Engineering Electromagnetics by Balanis (Advanced)

RF and Microwave Engineering

RF Circuit Design: Theory & Applications by Ludwig and Bogdanov
RF Circuit Design by Bowick
Foundations for Microwave Engineering by Collin
Microwave Engineering by Pozar
Microwave Filters, Impedance-Matching Networks, and Coupling Structures by Matthaei and Young

Antennas

Antenna Theory and Design by Stutzman and Thiele
Antenna Theory: Analysis and Design by Balanis
Antennas: For All Applications by Kraus and Marhefka

Radar Engineering

Introduction to Radar Systems by Skolnik
Fundamentals of Radar Signal Processing by Richards
Detection, Estimation, and Modulation Theory; Part I: Detection, Estimation, and Filtering Theory; Part III: Radar-Sonar Signal Processing and Gaussian Signals in Noise by Van Trees
Radar Handbook by Skolnik

Computational Electromagnetics

Computational Electromagnetics With MATLAB by Sadiku
Field Computation by Moment Methods by Harrington
Finite Element Method for Electromagnetics by Volakis, Chatterjee, and Kempel

Power Systems

Power System Analysis and Design by Glover, Sarma, and Overbye
Power System Analysis by Saadat
Modern Power System Analysis by Kothari and Nagrath
Power System Analysis by Grainger and Stevenson Jr

Electric Machinery

Electric Machinery Fundamentals by Stephen Chapman
Fitzgerald & Kingsley's Electric Machinery by Stephen Umans

Semiconductor Device Physics

Semiconductor Device Fundamentals by Pierret
Semiconductor Physics And Devices: Basic Principles by Neamen
Device Electronics for Integrated Circuits by Muller and Kamins
Advanced Semiconductor Fundamentals by Pierret
Physics of Semiconductor Devices by Simon M. Sze and Kwok K. Ng

Photovoltaic Cell Physics

Martin Green - Solar Cells: Operating Principles, Technology, and System Applications (Dated from the 1981 but good on the fundamentals)
Jenny Nelson - The Physics of Solar Cells: Photons In, Electrons Out
Peter Würfel - Physics of Solar Cells: From Basic Principles to Advanced Concepts

VLSI

Digital Integrated Circuits: A Design Perspective by Rabaey, Chandrakasan, and Nikolic
CMOS VLSI Design: A Circuits and Systems Perspective by Weste and Harris
Fundamentals of Modern VLSI Devices by Taur and Ning

Photonics and Optics

Fundamentals of Photonics by Saleh and Teich
Photonics by Yariv and Yeh
Introduction to Fourier Optics by Goodman
Modern Optical Engineering by Smith
Statistical Optics by Goodman
Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light by Max Born and Emil Wolf

Wireless Communications

Wireless Communications: Principles and Practice by Rappaport (Overview or supplement)
Wireless Communications by Molisch
Fundamentals of Wireless Communication by Tse and Viswanath

Information and Coding Theory

See the CS&E recommendations: Information Theory and Coding Theory

Speech Processing

Prerequisite: Digital Signal Processing

Theory and Applications of Digital Speech Processing (2010) by Rabiner and Schafer
Spoken Language Processing (2001) by Huang, Acero, and Hon
Discrete-time Speech Signal Processing (2001) by Quatieri

See also CS&E's Natural Language Processing

Control Theory

Modern Control Engineering by Ogata
Control Systems Engineering by Nise
Modern Control Theory by Brogan
Multivariable Feedback Control: Analysis and Design by Skogestad and Postlethwaite
Optimal Control Theory: An Introduction (Dover Books on Electrical Engineering) by Kirk
A Course in Robust Control Theory: A Convex Approach by Dullerud and Paganini

EMC & Signal Integrity

Electromagnetic Compatibility Engineering by Henry W. Ott (Updated version of Ott's "Noise Reduction Techniques in Electronic Systems")
Introduction to Electromagnetic Compatibility by Clayton R. Paul
High Speed Digital Design: A Handbook of Black Magic by Howard Johnson and Martin Graham
High-Speed Digital System Design: A Handbook of Interconnect Theory and Design Practices by Stephen H. Hall, Garrett W. Hall, and James A. McCall
Advanced Signal Integrity for High-Speed Digital Designs by Stephen H. Hall and Howard L. Heck

Websites