Dark matter particles must be electrically neutral; otherwise they would scatter light and thus not be "dark". They must also almost certainly be non-colored. With these constraints, the LSP could be the lightest neutralino, the gravitino, or the lightest sneutrino.
Sneutrino dark matter is ruled out in the MSSM because of the current limits on the interaction cross section of dark matter particles with ordinary matter as measured by direct detection experiments -- the sneutrino interacts via Z boson exchange and would have been detected by now if it makes up the dark matter. Extended models with right-handed or sterile sneutrinos reopen the possibility of sneutrino dark matter by lowering the interaction cross section.
Neutralino dark matter is the favored possibility. In most models the lightest neutralino is mostly bino (the superpartner of the hypercharge gauge boson), with some admixture of wino and/or Higgsino.
Gravitino dark matter is a possibility in supersymmetric models in which the scale of supersymmetry breaking is low, around 100 TeV. In such models the gravitino is very light, of order an eV. As dark matter, the gravitino is sometimes called a super-WIMP because its interaction strength is much weaker than that of other supersymmetric dark matter candidates. For the same reason, its direct thermal production in the early universe is too inefficient to account for the observed dark matter abundance. Rather, gravitinos would have to be produced through the decay of the next-to-lightest supersymmetric particle (NLSP).
In extra dimensional theories, their are analogous particles called LKP's or Lightest Kaluza-Klein Particle. These are the stable particles of extra-dimensional theories .