Science is inherently inductive: you collect data about things and try to reason from it, and you cannot (except in very rare cases) collect all possible data.
Bayesian analysis just provides a formal structure around your inductions that is different than the frequentist structure. It's still inductive at its heart in that you will conclude that X is true (p < whatever) on the basis of N examples. Regression, classification, and data mining as typically used all fall into this camp also--extrapolating or interpolating general patterns on the basis of a non-exhaustive set of samples. The cases where you have all examples and don't want to think about any more are pretty limited (but those could be deductive, strictly speaking).
Modeling is another area which may seem ambiguous. Most modeling is essentially deductive--given that we think we know X, Y follows in a non-obvious and perhaps computationally intensive way. But once you use your model to fill in for missing data, you're taking an inductive step.
However, I don't think that in actual practice scientists spend a lot of time worrying about the distinction between inductive and deductive modes of inquiry. A lot of the interesting questions involve both mixed in tremendously complicated ways (e.g. nonlinear systems research, with complex mathematics telling you the consequences of rules that you've derived inductively, etc.). Indeed, the whole idea of "propagation of error" highlights how induction (on data) and deduction (giving mathematical formulae) are frequently and deeply mixed. A scientist ought to spend his or her time considering estimates of errors rather than which steps are inductive and which deductive.
