So many people ask for book recommendations that I thought I'd write some down. This is not a complete list, just a random selection to help the kinds of people who usually ask me to recommend books. All of these books are well-written and among the very best I have come across. (Of course I haven't read everything yet, nor do I intend to.) I have no financial stake in any of these books.
Foundations of Applied Mathematics, Michael D. Greenberg, is wonderful, but sadly out of print. It covers all the basics that a Master's-educated applied mathematician should know. If you steal the library copy, you will make enemies.
Advanced Mathematical Methods for Scientists and Engineers, C. Bender and S. Orszag. Pay attention to the word "advanced". It is full of very useful methods you won't find in Greenberg's book.
Nonlinear Dynamics and Chaos, Steven Strogatz. A textbook suitable for upper-level undergraduates or beginning graduates in applied mathematics. Dynamical systems approach to the study of differential equations. Excellent pedagogy, abundant examples, many many applied problems. I somehow think the word "bifurcations" should be in the title, since that's a major theme and possibly the most important topic for most people. The book is so comfortable with applications that we use it as the text for our first-year graduate course in biomathematics.
Numerical Methods for Engineers and Scientists, Joe Hoffman. So you got your feet wet with Numerical Recipes. How do you really do numerical work? The Hoffman book has a huge variety of methods, and it's very well organized and easy to follow. The best part is the hundreds of figures illustrating iterations, which let you easily compare algorithms.
Numerical Computation in Science and Engineering, C. Pozrikidis. Another excellent book on numerical methods. Very clearly written and well organized.
Introduction to Theoretical and Computational Fluid Dynamics, C. Pozrikidis. The beauty of this book is that it abandons the classical approach of derivation of exact solutions of the few linear or weakly nonlinear problems that we can do, and integrates theory with computational methods and results, so you can quickly get to do CFD. Well written and organized.
The Visual Display of Quantitative Information and Envisioning Information by Edward Tufte. The world is full of so much information, and most of it is so badly organized and badly presented. Wouldn't you rather learn some basic design principles that will let you effectively communicate visually? A picture is worth a thousand words, but a bad picture is worth nothing.
Biomechanics and Biophysics
Biomechanics: Motion, Flow, Stress, Growth, Y-C Fung
Biomechanics: Mechanical Properties of Living Tissues, Y-C Fung
Biomechanics: Circulation, Y-C Fung
All the Fung books are wonderful, combining theoretical background and experimental results. An Introduction to Continuum Mechanics, Y.-C. Fung. Yet another great book by Fung. This is an undergraduate-level engineering text that isn't just about building bridges. There are excellent biological examples and exercises in it.
Life in Moving Fluids, 2nd ed. Steven Vogel. A spectacularly broad description of what happens when things flow in and around living things. The mathematical level is basic. This is not a book about theoretical or computational fluid dynamics.
Axis and Circumference, Stephen Wainwright. A short and sweet book exploring the implications of being cylindrical.
Biological Physics of the Developing Embryo, Gabor Forgacs and Stuart A Newman. A splendidly written, very accessible book about the physical forces that make us who we are. I believe that there is no other book out there on this topic at an introductory level.
Fiction About Science/Academia
Cantor's Dilemma, Carl Djerassi
The Bourbaki Gambit, Carl Djerassi
Menachem's Seed, Carl Djerassi
NO, Carl Djerassi
Djerassi's four novels (to be read in this order) are simultaneously about the culture of science, ethics, major discoveries, women in research, high culture, and occasionally politics and sex. Why not start a Djerassi book discussion group for students and/or faculty to discuss these issues?
Moo, Jane Smiley: a sly, very clever and accurate composite portrait of academic life, from housekeeping to Provost. If you have ever been at a university, you will enjoy it.
The curious incident of the dog in the nighttime by Mark Haddon. Not exactly about academia, but about people who can get obsessed about ideas. Features some well-known and interesting mathematics.
The Complete Guide to Landscape Design, Renovation, and Maintenance: A Practical Handbook for the Home Landscape Gardener by Cass Turnbull. Irreverent, practical, fun, and it's also good landscaping. By the founder of Seattle's PlantAmnesty ("One raging woman is a lunatic, 2000 people is a movement.") For anyone wondering why their yard doesn't look like the Arboretum. The publisher chose the title. Cass wanted to call it It's a Jungle Out There.
Getting What You Came For: The Smart Student's Guide to Earning a Master's or a Ph.D., Robert L. Peters.
The Elements of Style by William Strunk Jr., E.B. White, Roger Angell. Everybody has to learn to write, and if you write well, people will understand your work. If you write really well, people will seek out your work, cite it, fund it, and praise it, even if the work itself isn't good. If you write badly, people will not bother to read your work, and you will slowly and painfully fade away into obscurity and unemployment.
Ms. Mentor's Impeccable Advice for Women in Academia, Emily Toth. Irreverent and good advice for young and old, from students to Emeritae. Excellent advice in the grad student section.
A PhD is Not Enough: A Guide to Survival in Science by Peter Feibelman. A slim and overpriced book that is nonetheless worth the price for its excellent advice. Borrow it from a friend.