[mjw]

Pretty much any kind of mathematical modelling that involves uncertainty, really.

Making inferences and predictions from data, in the presence of uncertainty.

Analysis of the properties of procedures for doing the above.

If you want examples that avoid the feel of just "curve fitting" (assume you mean something like "inferring parameters given noisy observations of them") -- maybe look at models involving latent variables. Bayesian statistics has quite a few interesting examples.

[MichailP]

Thanks! I had a course at uni named Probability and Statistics, but since it was first (and only) course in EE curriculum it was oriented toward probability, and Statistics was an afterthought (I only remember simple linear and multilinear regression). That is probably the main reason I only see curve fitting everywhere :)