In 2010, there are at least twelve states, plus the District of Columbia, that have held contested primaries for minor parties:

Arizona had a 4-way gubernatorial primary for the Libertarian Party; California held contested primaries for all four of its ballot-qualified minor parties; Colorado held statewide Libertarian primaries; the District of Columbia is about to hold contested primaries for the Statehood Green Party; Florida held a contested state legislative primary for the Libertarian Party; the Illinois Green Party primary had a few contests for district office; Louisiana held a U.S. Senate primary for the Libertarian Party; the Maine Green Party had two contested legislative races; Minnesota had a contested gubernatorial primary for the Independence Party; Missouri had a contested Libertarian primary for several offices, including U.S. Senate; New York is about to hold a contested gubernatorial primary for the Conservative Party; Ohio had a few contested district office Libertarian primaries; and Vermont had several statewide contested Liberty Union primaries.  Thanks to the posters below for help with this blog post.

This is believed to be the highest number of states that have held contested minor party primaries in a midterm year since before World War II.  States that have held contested minor party primaries (for office other than President) since World War II, but not this year, are Alaska, Connecticut, Hawaii, Oklahoma, Pennsylvania, Washington, and possibly others.