What proteins are important in addiction?

Not really . It is the experimentation and socio economic status that plays a major role.
BDNF, NF-KB & more! Since addiction involves multiple pathways in the brain and substantially cell-level changes, many proteins are under investigation for their involvement in addiction. A couple interesting ones include bdnf (a neurotrophic factor, i.e. A protein that helps neurons grow & alters their function) and nf-kappa b (a protein involved in the innate immune system, which may be activated during addiction).