Disclaimer: Highly subjective personal opinion follows...
For theory and applications I can't recommend Generalized Linear Models and Extensions by Hardin and Hilbe too highly. It uses
SPSS Stata, (both of) which I never use and know nothing about, but it covers the theory and has a very rich set of examples. If I had to choose one book to start with, it would be this one.
A more theory-focused book is Generalized, Linear, and Mixed Models by McCulloch, Searle, and Neuhaus. This has fewer examples than Hardin and Hilbe but goes further into random effects for both the linear model and the GLM. This is my favorite GLM book, because it connects a lot of things together, but if you have no interest in random effects it may be overkill.
What I would call a canonical reference for GLMs is Generalized Linear Models by McCullagh and Nelder. It's a little older title but I enjoyed it very much.
Generalized Linear Models with Applications in Engineering and the Sciences by Myers, Montgomery, Vining, and Robinson spends a little more time on the binary/poisson GLMs and also has interesting examples. The new edition has examples in a few languages, including R.
I picked up Faraway's Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models a while back, and it has been very useful for helping me do things in R, though it's not a good "teach yourself GLM" book. But it may be a good companion to some of the other books out there.