When do I need a model? Considering the scenarios of exploring data, predicting (in the range of predictors), extrapolating and explaining- for which would one need a model? When can one do without one?
[Edit] By "model" I mean a probabilistic representation of the data generating process.
As an example I would say, that for the purpose of exploratory data analysis, one can do nicely without a model (exceptions do exist), and for the purpose of making predictions "out of data" (extrapolation), one will not get very far without one. What more can be said about the different scenarios?
 A: Can you give your definition of model? I would say even in EDA we almost always use models (say fit a Loess line to a scatterplot, or kernel density estimate the PDF of a distribution, or identify outliers via some criterion), although they may be more implicit than explicit.
In the process of data reduction one takes a larger set of data and reduces it down into smaller sets of information that can be easily processed or understood. These smaller sets of information can be estimates of model parameters, or they can be reduced sets of information in graphical displays (they aren't really different though, to reduce the information in essence takes a model).
So to directly answer your question, I would say anytime you can not tell everything you want to know from your data by simply examining scatterplots or histograms of the distributions, then some type of model is necessary. Which given that definition I have personally never come across such a situation in which I did not need some type of model.
