The explanation for the observed light neutrino masses that involves massive right-handed neutrinos is called the "seesaw mechanism", since it kind of works like a seesaw (when mass of right-handed neutrinos goes up, the left-handed neutrino masses go down. Since observed neutrino masses are very very light, like ridiculously so, it was first though that they were massless until it was discovered that they oscillate between 3 flavours, which is only possible if they have mass, these right-handed neutrinos must be quite massive indeed)

For the record, I'm not a particle physicist of any kind and I got that information from a couple lectures that I watched that were about neutrino-related things.

The supersymmetry camp also thinks that right-handed sneutrinos (the theoretical supersymmetric partners of the neutrinos) could also be a candidate for dark matter. Note the prefixed s, that's how most of the supersymmetric partners of the observable fermions are named (squarks, selectrons, sneutrinos), while most of the supersymmetric partners of the observable bosons end with ino (photino, gravitino, and I'm pretty sure they call the partner of the W boson the Wino).