I've seen OPEs commonly used in 2d CFT, it's quite apparent to me that, in that case, it dresses a bridge between the algebraic and the operator formalism especially when combined with radial ordering and the use of contour integral. Even more powerful in the minimal models where it leads to the bootstrap equations and the resolution of the 3 pt functions. I also heard that OPE are sometimes used in other circumstances, for instance in the QCD chapter of Peskin & Schroeder's book but I don't recall the motive. I'd be curious to know what generally it is relevant to decompose the products of operators into an "operator basis" ie. associate an algebra to the space of operators.
My memory of Peskin & Schroder is a little hazy, but they're probably discussing the Shifman-Vainshtein-Zakharov sum rules. The idea is that you can use the OPEs for composite operators representing mesons/hadrons to derive formulae that express meson/hadron n-point functions in terms of the VEVs of various QCD condensates. (Edit: Just discovered that Shifman has some very nice lecture notes on the subject.)
More generally: OPEs are always relevant (if not always easy to use in a given situation) because they carry almost all the information about a field theory. You can actually define a QFT by writing down the set of local observables, the OPEs between them, and the VEVs of the local observables. It's as good a formalism as the Hamiltonian or path integral formalisms -- better in some ways, because it applies when the path integral doesn't.