While visiting 1986 Earth, James T. Kirk described to Gillian Taylor why he was so interested in George and Gracie. When Kirk asked Taylor if she wanted the details, she told him, "I wouldn't miss this for all the tea in China." (Star Trek IV: The Voyage Home)
During San Francisco's Bell Riots, in 2024, Biddle Coleridge commented on the television coverage of the hostage situation, stating that "great, we're on every channel. I bet they're watching this in China." (DS9: "Past Tense, Part II")
A 21st century-era political map of Earth was stored in the USS Enterprise's library computer in 2254. The location of China was labeled on this map. This map was among the materials viewed by the Talosians when they scanned the Enterprise computer. (TOS-R: "The Cage")
In 2365, Picard, commenting on the hitherto indeterminate location of Iconia, reminded Wesley Crusher that China, too, had been thought a myth until Marco Polo reported his own journey there. (TNG: "Contagion")
Background information Edit
The map used in the remastered "The Cage" was a Central Intelligence Agency map published in September 2008. The ice shelfs of Antarctica were masked with black ink. Beijing was labeled on the map; its location was represented by a black star. 
Retroactive continuity: A 20th century-era map of the North Pacific Ocean region, depicting the east coast of Asia and Alaska on the west coast of North America, was stored in the USS Enterprise's library computer in 2254. This map was among the materials viewed by the Talosians when they scanned the Enterprise computer. (TOS-R: "The Cage")
Early drafts of Star Trek: First Contact were to have said that China was a leading member of the Eastern Coalition in the Third World War, but it was decided that politics didn't really matter to the story, so the lines were cut.