We study numerically the Kawasaki dynamics of the 2D Ising model. At large time we recover the coarsening growth as l(c)(t) proportional t(1/3). At shorter time however, the system enters a metastable glassy regime that displays an extremely slow growth and nontrivial violations of the fluctuation-dissipation theorem similar to those observed in spin glasses: this is one of the simplest systems in which such violations occur. We also consider Potts models, where a similar behavior is observed, and the model of Shore and Sethna where the domain growth is also slow, but where violations of the fluctuation-dissipation theorem are trivial. We finally comment on these violations in the context of activated coarsening, and on similarities and differences with the glass transition phenomenology.