It depends on what state (and what office)? Laws vary state by state usually determined by what the parties decide. On the presidential level, independents can currently vote in 33 states in the (Democratic) Primary (there's a few states, e.g. California, where it's open in one party and closed in the other) and closed in 17. In Idaho, the Republican Party is trying to close down a primary that has been open for many years and independents (led by the Committee for A Unified Independent Party (www.independentvoting.org) and the Amnerican Independent Movement of Idaho intervened on the suit and won the right for the first time for independents who are not a party to be party to a suit of this kind). And there are several states (e.g. Kentucky) where legislation has recently been introduced