Probability and Statistical Inference by R. V. Hogg & E. Tanis (2009, 8th ed.)  Popular undergraduate text with wide scope.

Mathematical Statistics and Data Analysis by J. A. Rice (2006, 3rd ed.)  Widely respected undergraduate text with wide coverage.

A First Course in Probability by S. Ross (2009, 8th ed.)  Strong text on the foundations of probability theory.

Graduate texts with broad coverage

Introduction to Mathematical Statistics by R. Hogg, J. McKean & A. Craig (2012, 7th ed).  Standard respected text for graduate students in statistics, heavy on mathematical theory.

Introduction to Probability Models by S. M. Ross (10th ed., 2010) Widely used text covering random variables, Markov chains, queueing theory, stochastic processes, simulation techniques.

All of Statistics: A Concise Course in Statistical Inference by L. Wasserman (2010)  Short text intended for graduate students in allied fields with emphasis on mathematical foundations.

Essential Statistical Inference: Theory and Methods by D. D. Boos and L. A. Stefanski (2013)  A new text covering likelihood-based methods, Bayesian inference, large sample theory, M-estimation, misspecified models, jackknife and bootstrap, permutation and rank tests (with R code).

Methods of Statistical Model Estimation by J. M. Hilbe & A. Robinson (2013, forthcoming)  With R scripts.

Nonparametric statistics

Practical Nonparametric Statistics by W. J. Conover (3rd ed., 1999) Respected presentation of classical nonparametrics.

An Introduction to Modern Nonparametric Statistics by J. J. Higgins (2004)  Undergraduate text.

Applied Nonparametric Statistical Methods by P. Sprent & N. C. Smeeton (4th ed., 2009)  Single, 2- and k-sample inference; survival data; correlation and bivariate regression; categorical data; robust estimation.

Bayesian inference

Bayesian Data Analysis by A. Gelman, J. B. Carlin, H. S. Stern & D. B. Rubin (2nd ed., 2003)  Comprehensive and useful volume.

The BUGS Book: A Practical Introduction to Bayesian Analysis by D. Lunn, C. Jackson, N. Best, A. Thomas & D. Spiegelhalter (2012).  By the developers of BUGS software (Bayesian Inference Using Gibbs Sampling) with worked examples and exercises.

Bayesian Methods for Data Analysis by B. P. Carlin & T. A. Louis (3rd ed., 2008)  Introduction to Bayesian analysis, hierarchical modeling, Markov chain Monte Carlo methods, with solutions manual. Applications in biostatistics.

Doing Bayesian Data Analysis: A Tutorial with R and BUGS by J. K. Kruschke (2010)  Basics of Bayesian inference, Gibbs sampling, hierarchical modeling, model comparison, hypothesis testing, contingency tables applied to the problems of binomial proportions and generalized linear modelling.

Density estimation

Multivariate Density Estimation: Theory, Practice and Visualization, by D. W. Scott (1992).  Nonparametric density estimation (data smoothing) techniques.

Multivariate analysis (regression, clustering)

Applied Linear Statistical Models by M. H. Kutner, C. J. Nachtsheim, J. Neter & W. Li (5th ed., 2005)  Comprehensive undergraduate text

A Modern Approach to Regression with R by S. J. Sheather.  Practical introductory monograph with R scripts.

Applied Multivariate Statistical Analysis by R. A. Johnson & D. W. Wichern (6th ed., 2007). Popular undergraduate text.

Logistic Regression Models by J. M. Hilbe (2009)  Treating regression with binary or categorical response variables, topics include least squares and maximum likelihood estimation, goodness-of-fit, overdispersion.  Scripts given in R, Stata and other languages.

Negative Binomial Regression by J. M. Hilbe (2nd ed., 2011) Comprehensive presentation of methods of regression involving Poisson count response variables.  Topics include contingency tables, regression modeling, model fit tests,  overdispersion, zero counts, censoring & truncation, and latent variables.

Bayesian and Frequentist Regression Models by J. Wakefield (2013)  A comprehensive and modern treatment with Bayesian and frequentist techniques viewed as complementary.  Topics include linear and nonlinear modeling, binary data models, conditional likelihood inference, hyperpriors, nonparametric regression, shrinkage methods, spline and kernel methods, and classification.

Cluster Analysis by B. S. Everitt, S. Landau, M. Leese & D. Stahl (5th ed., 2011)  Undergraduate-level text on multivariate clustering, mixture models, and related methods

Data mining (regression, clustering, classification)

Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning by A. J. Izenman (2008) Comprehensive graduate text with broad coverage.

Pattern Classification by R. O. Duda, P. E. Hart & D. G. Stork (2nd ed., 2001)  Comprehensive and respected graduate text on machine learning techniques.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction by T. Hastie, R. Tibshirani & J. Friedman (2nd ed., 2009) Respected advanced monograph by distinguished statisticians.

Machine Learning: An Algorithmic Perspective by S. Marsland (2011).  Monograph on methodology of data mining methods.

Introduction to Data Mining by P.-N. Ting, M. Steinbach & V. Kumar (2005)  Popular volume covering clustering methods, kernel methods, outlier detection, regression, optimization.  Pseudo-code provided.

Survival analysis (for upper limits)

Survival Analysis: Techniques for Censored and Truncated Data by J. P. Klein & M. L. Moeschberger (2010)  Comprehensive graduate textbook.

Statistical Models and Methods for Lifetime Data by J. F. Lawless (2nd ed., 2003)  Comprehensive advanced monograph.

Data visualization

Handbook of Data Visualization edited C. Chan, W. Hardle & A. Unwin (2008)  Review articles on modern visualization techniques.

Time series analysis

The Analysis of Time Series: An Introduction by C. Chatfield (6th ed., 2004) Undergraduate-level textbook.

Time Series Analysis and Its Applications with R Examples by R. H. Shumway & D. Stoffer (3rd ed., 2011) Graduate-level text with R scripts.

Time Series Analysis: Univariate and Multivariate Methods by W. W. S. Wei (2nd ed. 2006)  Advanced monograph.

A Wavelet Tour of Signal Processing: The Sparse Way by Stephane Mallat, (3rd ed., 2009)  Graduate textbook.

Spatial analysis

Spatial Analysis: A Guide for Ecologists by M. J. Fortin & M. Dale (2005) Introductory text

The SAGE Handbook of Spatial Analysis edited by A. S. Fotheringham & P. A. Rogerson (2009)  Review articles from a geographic perspective

Statistical Analysis and Modelling of Spatial Point Patterns by J. Illian, A. Pentinnen, H. Stoyan & D. Stoyan (2008)  Comprehensive advanced monograph on modern methods

Statistics for Spatial Data by N. Cressie (1993)  Graduate text covering spectral theory, simulation methods, spatial bootstrapping, image analysis, and computational methods.

Handbook of Spatial Statistics edited by A. E. Gelfand, P. Diggle, P. Guttorp and M. Fuentes (2010).  Collection of review articles on likelihood models, spectral models, hierarchical modeling, spatial autocorrelation, spatial point process theory and models, parametric and nonparametric models, multivariate models and spatio-temporal processes.

Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications by Marinucci, D and G. Peccati (2011).  Mathematical treatment of graphical models, spectral representations, characterizations of isotropy, Gaussian random fields, sample power spectrum and bispectrum, spherical needlets, and spin random fields.

R statistical software environment

R in a Nutshell, J. Adler (2nd ed., 2012).  Comprehensive reference book

Software for data analysis: Programming with R by J. M. Chambers (2010) Authoritative guidance on R programming by the originator of S and R.

The Art of R Programming: A Tour of Statistical Software Design by N. Matloff (2011) Elementary and advanced techniques

Introductory Statistics with R by P. Dalgaard (2008)  Elementary presentation by a founder of R.

A First Course in Statistical Programming with R by W. J. Braun and D. J. Murdoch (2010).  A slim volume emphasizing programming techniques including simulation, computational linear algebra, and numerical optimization.

Modern Applied Statistics with S by W. N. Venables & B. D. Ripley (2002)  Important methods and R scripts explained

Statistical Modelling in R by M. Aitkin, B. Francis, J. Hinde and R. Darnell (2010)  Volume introduces R and statistical inference; regression; analysis of variance; binary, multinomial and Poisson data, survival data, finite mixture models, random effects models, and variance component models.

Data Analysis and Graphics Using R: An Example-Based Approach by J. Maindonald & W. J. Braun (3rd ed., 2010).  Includes reviews of R and inference, bivariate and multivariate regression, generalized linear modeling, survival analysis, time series modeling, multi-level modeling, tree classification and regression, data mining

Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models by J. J. Faraway.  A more advanced treatment covering binomial data, count (Poisson) regression, contingency tables, multinomial data, generalized linear models, random effects, longitudinal data, nonnormal responses, nonparametric regression, additive models, trees and neural networks.

Introduction to Scientific Programming and Simulation Using R by O. Jones, R. Maillardet & A. Robinson (2009)  R data structures and programming, numerical techniques, optimization, basic probability, Monte Carlo simulations, variance reduction.

Use! R series by Springer publishers.  A large series (currently >40 volumes) of short focussed volumes with methodology and R scripts. Topics include solving differential equations, graphical models, data mining with Rattle, probability simulation & Gibbs sampling, Monte Carlo methods, ggplot2 graphics, time series, Bayesian computation, nonlinear regression, spatial analysis, wavelet methods, ggobi dynamic graphics.