Feature selection for Support Vector Machines
Personally, I like to divide feature selection in two:


unsupervised feature selection
supervised feature selection


Unsupervised feature selection are things like clustering or PCA where you select the least redundant range of features (or create features with little redundancy). Supervised feature selection are things like Lasso where you select the features with most predictive power.

I personally usually prefer what I call supervised feature selection. So, when using a linear regression, I would select features based on Lasso. Similar methods exist to induce sparseness in neural networks.

But indeed, I don't see how I would go about doing that in a method using kernels, so you are probably better off using what I call unsupervised feature selection.

EDIT: you also asked about regularization. I see regularization as helping mostly because we work with finite samples and so the training and testing distribution will always differ somewhat, and you want your model to not overfit. I am not sure it removes the need to avoid selecting features (if you indeed have too many). I think that selecting features (or creating a smaller subset of them) helps by making the features you do have more robust and avoid the model to learn from spurious correlations. So, regularization does help, but not sure that it is a complete alternative. But I haven't thought thoroughly enough about this.