10 types of regressions. Which one to use?

The CRAN task view: "Robust statistical methods" gives a long list of regression methods, including many that Vincent mentions. Here a some that are not mentioned there: Regression in unusual spaces. It is usually addressed under the title "Compositional data" (see Wikipedia entry). The late John Aitchison founded this area of statistics. Googling his name "compositional data" gives access to a number of his articles.