What are modern, easily used alternatives to stepwise regression? I have a dataset with around 30 independent variables and would like to construct a generalized linear model (GLM) to explore the relationship between them and the dependent variable.
I am aware that the method I was taught for this situation, stepwise regression, is now considered a statistical sin.
What modern methods of model selection should be used in this situation?
 A: @johannes gave an excellent answer. If you are a SAS user, then LASSO is available through PROC GLMSELECT and partial least squares through PROC PLS.
David Cassell and I made a presentation about LASSO (and Least Angle Regression) at a couple of SAS user groups. It's available here
A: There are several alternatives to Stepwise Regression. The most used I have seen are:


*

*Expert opinion to decide which variables to include in the model.

*Partial Least Squares Regression. You essentially get latent variables and do a regression with them. You could also do PCA yourself and then use the principal variables.

*Least Absolute Shrinkage and Selection Operator (LASSO). 


Both PLS Regression and LASSO are implemented in R packages like 
PLS: http://cran.r-project.org/web/packages/pls/ and 
LARS: http://cran.r-project.org/web/packages/lars/index.html
If you only want to explore the relationship between your dependent variable and the independent variables (e.g. you do not need statistical significance tests), I would also recommend Machine Learning methods like Random Forests or Classification/Regression Trees. Random Forests can also approximate complex non-linear relationships between your dependent and independent variables, which might not have been revealed by linear techniques (like Linear Regression). 
A good starting point to Machine Learning might be the Machine Learning task view on CRAN: 
Machine Learning Task View: http://cran.r-project.org/web/views/MachineLearning.html
A: Another option you might consider for variable selection and regularization is the elastic net. It's implemented in R via the glmnet package.
A: Model averaging is one way to go (an information-theoretic approach). The R package glmulti can perform linear models for every combination of predictor variables, and perform model averaging for these results. 
See http://sites.google.com/site/mcgillbgsa/workshops/glmulti 
Don't forget to investigate collinearity between predictor variables first though. Variance Inflation Factors (available in R package "car") are useful here.
A: Interesting discussion. To label stepwise regression as statistical sin is a bit of a religious statement - as long as one knows what they are doing and that the objectives of the exercise is clear, it is definitely a fine approach with its own set of assumptions and, is certainly biased, and does not guarantee optimality, etc. Yet, the same can be said of of lot of other things we do. I have not seen CCA mentioned, which addresses the more fundamental problem of the correlation structure in covariate space, does guarantee optimality, has been around for quite a bit, and it has somewhat of a learning curve. It is implemented on a variety of platforms including R.
