North Dakota (open caucus)
South Carolina (modified open primary)
Washington (modified open)
Michigan (modified open)
Virginia (open)
Wisconsin (open)
Idaho (open)
Utah (modified open)
California (modified open)
Georgia (open)
Massachusetts (modified open)
Minnesota (modified open)
Ohio (modified open)
Rhode Island (modified open)
Vermont (open)
Kansas (modified open)
Illinois (open)
North Carolina (modified open)
Indiana (modified open)
North Carolina (modified open)
Nebraska (mod. open)
West Virginia (mod. open)
Arkansas (open)
Alabama (open)
Montana (open)
This list is from a cursory check.
Here is the definition of "modified open:"
http://www.thegreenpapers.com/Definitions.html#ModiMODIFIED OPEN PRIMARY OR CAUCUS
In a Modified open Primary or Caucus, persons registered with one of the major parties usually may only vote in that party's primary: generally, Democrats may only vote in the Democratic primary, while Republicans may only vote in the Republican primary. However, unlike in a Closed Primary or Caucus, Independents may choose to vote in either party's primary - though there are usually provisions which automatically make an Independent a registered member of whichever party the primary of which he or she has chosen to vote in: this tends to keep the number of Independents who take advantage of their privilege to vote in a Modified open primary or caucus relatively low (making what is called a Modified open primary or caucus, in fact, more of a "modified closed primary or caucus" in its actual operation!)
However, in some Modified Open states, a Democrat voting in the Republican primary or a Republican voting as a Democrat automatically changes one's party affiliation as well; this has tended to reduce such "crossover voting" between the two major parties in those Modified Open states which practice this automatic change in party registration- for many registered party members might very well think twice before casting a primary vote which would have such an impact on their party affiliation.