Answer to today's ICJ inquiry puzzler above:
The only nation-state that has declined to appear since 1981 in a case before the International Court of Justice is the United States of America. See Christopher Greenwood, "The Role of the International Court of Justice in the Global Community," 17 U.C. Davis J. Int'l L. & Pol'y 233, 250 n.64 (2011), a publication based on a lecture about which we've posted here and here.
As students of international law well know, the case was Nicaragua v. United States (1986), about which we've posted here, here, and here.