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?