Chemical Engineering

Safety First

Chemical Process Safety: Fundamentals with Applications by Crowl and Louvar
System Safety Engineering And Risk Assessment: A Practical Approach by Bahr
System Reliability Theory: Models, Statistical Methods, and Applications by Rausand and Høyland
Technology, Law, and the Working Environment by Ashford and Caldart

Fundamentals

Prerequisites

For almost all these books, a working knowledge of Introductory Physics, General Chemistry, Multivariable Calculus, Ordinary Differential Equations and Partial Differential Equations is assumed. A general engineering foundation in Statics, Mechanics of Materials, Material Science is important to reactor and unit operation design. Furthermore, chemical engineers are expected to pick up Organic Chemistry and Quantum Chemistry (the Thermal Chemistry section in Physical Chemistry is superseded by Chemical Thermodynamics below) as they progress but it is not immediately necessary and could be done at anytime. Knowledge of Linear Algebra, programming (Matlab tends to be the most popular but C++ isn't unheard of either), and Numerical Methods (especially involving DEs) is essential for professional chemical engineering.

Bible

Perry's Chemical Engineers' Handbook by Green and Perry

Material and Energy Balances

Elementary Principles of Chemical Processes by Felder and Rousseau
Basic Principles and Calculations in Chemical Engineering by Himmelblau and Riggs

Chemical Thermodynamics

Introduction to Chemical Engineering Thermodynamics by Smith, Ness, and Abbott
Molecular Engineering Thermodynamics by Pablo and Schieber
Engineering and Chemical Thermodynamics by Koretsky
Molecular Thermodynamics of Fluid-Phase Equilibria by Prausnitz, Lichtenthaler, and de Azevedo

Transport Phenomena

Transport Phenomena by Bird, Stewart, and Lightfoot
An Introduction to Mass and Heat Transfer: Principles of Analysis and Design by Middleman
Analysis of Transport Phenomena by Deen
Advanced Transport Phenomena by Slattery

See the Mechanical Engineering's Heat Transfer and Fluid Mechanics recommendations as well

Separation Processes

Transport Processes and Separation Process Principles (Includes Unit Operations) by Geankoplis
Separation Process Principles: Chemical and Biochemical Operations by Seader, Henley, and Roper
Separation Process Engineering: Includes Mass Transfer Analysis by Wankat (Additional reference for unit-operations)

Process Control

Process Dynamics and Control By Seborg, Edgar, Mellichamp, and Doyle
Process Control: Designing Processes and Control Systems for Dynamic Performance by Marlin

Reactor Design

Elements of Chemical Reaction Engineering by Fogler
Biochemical Engineering: A Textbook for Engineers, Chemists and Biologists by Yoshida and Katoh (important supplement to Fogler for covering Bioreactors)
Chemical Reaction Engineering by Levenspiel
Chemical Reactor Analysis and Design by Froment, Bischoff and De Wilde