A theory that cannot be tested experimentally is a very unsatisfying theory. The most interesting baryogenesis mechanisms are those that can be tested in terrestrial experiments.
In the next generation of collider experiments, at the Large Hadron Collider, the parameter space for standard-model electroweak baryogenesis will be fully explored; either it will be found that SM baryogenesis can account for the observed baryon asymmetry, or SM baryogenesis will be ruled out. As for the supersymmetric extensions to the SM electroweak mechanism, we will certainly know a great deal more than we currently do, perhaps enough to say whether it can account for the asymmetry. The detailed knowledge about the scalar quark fields that we hope to gain at the LHC will also be useful in fleshing out the Affleck-Dine mechanism.
The near future also looks promising in the neutrino sector, where
experiments currently being planned will measure the magnitude of
neutrino violation. This measurement could tell us that the
neutrino sector provides the required amount of violation for
leptogenesis.