California decline-to-state voters can choose which party primary they want to vote in, and all voters can vote for referendums like Proposition 14.
Iowa independents have to change their registration at the polling site to vote in caucuses.
Maine independents have to enroll in the party of the primary you want to vote in at the poll and have to re-register out of the party afterwards.
New Jersey has
Nevada independents cannot vote in the "member's only".
North Dakota indies can vote in open caucuses.
South Carolina indies can vote in the party primary of their choice; SC has nonpartisan registration.
South Dakota independents can vote in Democratic primaries, not in Republican primaries.
Virginia has nonpartisan elections, and everyone can vote in the party primary of their choice.
Also see OpenPrimaries.org