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We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behavior of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular attention is focused on those scalar-tensor theory cosmological models, which are shown to be self-similar, that correspond to general relativistic models that play an important role in describing the asymptotic behavior of more general models (eg, those cosmological models that act as early-time and late-time attractors).