Your thread title and poll question differ; states (or any gov't body) have no rights and only the power that the people allow them to have. Our U.S. constitution grants specific and limited powers to the federal gov't and reserves all other power to the people or to the several states. I will however discuss each item in your poll:
Abortion - as an elective medical procedure can be regulated by the state to help ensure that it is practiced safely and by knowedgable people. No state should be able to ban abortion or any other elective medical procedure.
Marriage - as a contract between consenting adults it is wiithin the power of the state to settle contract disputes.
Slavery - ownership of people should remain illegal and be enforced by all levels of gov't.
Narcotics consumption - I assume that you mean for personal recreational use should be left up to the individual. The production and distribution can be controlled by the state (as we now have for alcohol).
Adoption - similar to marriage, but the state may act as an agent for minors under the age of consent.
Trade & commerce - The gov't has far too much power in this area now; most trade regulation seems to serve to keep competition down and favor the larger existing businesses by imposing a ridiculous number of hoops to jump through in order for a new entity to try to gain a foothold. Outside of zoning laws and protection of the consumer (and general public) from dangerous practices or misleading claims the gov't should stay out of the way.
Immigration - the policy should be set federally and the states encouraged to help in the enforcement of that policy.
Education - the highest level of gov't involved should be the state but I prefer more local (county, city or school district control).
Religion - the 1st amendment covers this well by protecting the individual's right to freely practice their religious beliefs and prohibiting the gov't from establishing an "official" religion. The problem occurs when the religion defines taboos and the "religious" attempt to enforce those taboos on others. Your right to be faithful to your god ends where it impacts my right to live, act and believe as I choose.