Generalized linear models (GLM) relax the assumptions of standard linear regression. In particular, there are GLMs that can be used to predict discrete outcomes and model continuous outcomes with nonconstant variance. In the era of sophisticated machine learning predictors, linear models have somewhat fallen out of favor, but they're still very useful in situations where there is little data, prediction is not the inferential goal, or speed is of paramount importance.
Recommended Books

An Introduction to Generalized Linear Models
Annette J. Dobson and Adrian G. Barnett
Key Features
 Intext exercises
 R and WinBUGS code examples
Key Topics
 Analysis of Variance/Covariance
 Bayesian Analysis
 Clustered and Longitudinal Data
 Collinearity
 Diagnostics
 Exponential Family Distributions
 Goodness of Fit Statistics
 Hypothesis Testing
 Inference
 LogLinear Models
 Logistic Regression
 Markov Chain Monte Carlo Methods
 Maximum Likelihood Estimation
 Model Fitting
 Multiple Linear Regression
 Normal Linear Models
 Normal and Related Distributions
 Ordinal Logistic Regression
 Poisson Regression
 Repeated Measures Models
 Survival Analysis
Description
This is our goto book for GLM. The text includes a good review of linear models based on the normal distribution, model fitting, logistic regression and Poisson regression, as well as some bonus topics such as survival analysis. Our favorite part is that there is a fullfledged Bayesian treatment of some GLMs. This book is fairly mathematical for an introduction to an applied topic, but it is very readable.

Foundations of Linear and Generalized Linear Models
Alan Agresti
Key Features
 Intext exercises
 Some exercise solutions
 R example code
Key Topics
 Bayesian Linear Modeling
 Binary Data Modeling
 Confidence Intervals and Prediction Intervals
 Correlated Responses
 Exponential Family Distributions
 Hypothesis Testing
 Inference
 Least Squares Model Fitting
 Logistic Regression
 Models for Count Data
 Negative Binomial Regression
 Nominal Response Models
 Normal Linear Models
 Ordinal Response Models
 Poisson Regression
 Probit Regression
 QuasiLikelihood Methods
 Residuals, Leverage, and Influence
 Robust Regression
Description
This is a gentler book on GLMs than our main pick. Agresti is a great author (he has written several other excellent statistics books as well), and this book is a great overview of linear and generalized linear models. It doesn't have the same coverage as Dobson and Barnett (in particular, it doesn't have the same amount of Bayesian material), but it does have solutions to some exercises, which makes it great for the autodidact.