Dislocations

J. P. Hirth and J. Lothe, Theory of Dislocations, (Wiley, New York, 1982). This is the "Bible" for research in dislocations. It may be somewhat difficult to read if you do not have background in dislocations.
D. H. Hull and D. J. Bacon, Introduction to Dislocations, 4th ed. paperback. This book provides a good entry-level introduction to dislocations. It is recommended as a first read if you do not have previous background in dislocations.
J. Weertman and J. R. Weertman, Elementary Dislocation Theory,(Oxford University Press, 1992, paperback). Another reasonable introductory text to dislocations. Chris and Keonwook both started learning dislocation theory from this book. This book costs less than $40!
V. V. Bulatov and W. Cai, Computer Simulations of Dislocations (Oxford University Press, 2006). This book provides numerical models and algorithms useful for modeling dislocations at atomistic and continuum level.

Materials Science

Y.-M. Chiang, W. D. Kingery, D. P. Birnie, Physical Ceramics. This book provides the basic materials science background in ceramics. It is important if your research is in solid oxide fuel cells.
S. Suresh, Fatigue of Materials, 2nd ed. (Cambridge University Press, 1998). A must read if your research is related to metal fatigue.
G. E. Dieter, Mechanical Metallurgy, 3rd ed. (McGraw-Hill, 1986). Covers all aspects of mechanical deformation of metals --- e.g. continuum plasticity, dislocations, cracks, fatigue, creep, mechanical tests, metal forming. Comprehensive and easy to read.
I. V. Markov, Crystal Growth For Beginners, 2nd ed. (World Scientific, 2003). Very good book --- though you need to have a good background in thermodynamics and statistical mechanics. The book has 546 pages in total.

Computer Simulations

M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, (Oxford University Press, 1989). This is the classic text on molecular simulations. But since it is about 20 years old, several important methods are not discussed in this book.
D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed. Academic Press, San Diego, CA, 2002. This book provides an update to Allen and Tildesley's book with discussions on more advanced algorithms. It is a good reference but may be too advanced if you did not have any background in molecular simulations.
J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. Springer, 2006. This book explains the ideas behind the algorithms very clearly. Preview on Google books

Statistical Mechanics

J. P. Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity, (Oxford University Press, 2006). PDF available
D. Chandler, Introduction to Modern Statistical Mechanics, (Oxford University Press). Somewhat advanced, but very interesting to read. This is the book that Spider man uses when studying nanotechnology.
J. D. Gunton and M. Droz, Introduction to the Theory of Metastable and Unstable States, Lecture Notes in Physics, v. 183 (Springer-Verlag). An advanced and comprehensive review of nucleation theories. PDF available

Electronic Structure

R. G. Parr and W. T. Yang, Density-functional theory of atoms and molecules, International Series of Monographs on Chemistry, v. 16 (Oxford, 1989). Includes an introducion of density matrices and second quantization. PDF available

Experimental Data