The Communist Party announced earlier this month that it will no longer produce a paper edition of its weekly newspaper, the People’s Weekly World. The paper will be an internet publication.
Very few nationally-organized political parties in the United States continue to publish a paper edition of a national newsletter or a national newspaper. The Libertarian Party still publishes the Libertarian Party News on paper (monthly), and the Socialist Workers Party still publishes The Militant on paper (weekly). UPDATE: also the Party for Socialism and Liberation publishes a bi-weekly newspaper called Liberation, and has done so for the last two years.
The Green Party no longer publishes the Green Pages on paper, except on rare occasions. The Constitution Party has never had a paper periodical, although William Shearer’s former print publications unofficially served as national party publications. The Reform Party never had a periodical either, nor did the Natural Law Party.