Only one US Naval ship is held captive by another nation. N. Korea took the USS Pueblo in 1968 and uses it as a tourist attraction!
The US Navy is impressive. In terms of battle fleet tonnage, it is larger than the next 13 largest navies combined and operates 285 ships and 3,700 aircrafts. So it makes sense that US Naval ships aren't often captured. In fact, there is only one current US Naval vessel held captive, the USS Pueblo.
In January 1968, in what came to be known as the Pueblo incident or the Pueblo crisis, the North Koreans boarded and captured the USS Pueblo. They claimed that it had strayed into their waters, but the US maintains that they were still in international waters.
North Korea still has possession of the USS Pueblo, but is officially listed as a commissioned vessel of the US Navy. It's anchored in the Taedong River and is used as a museum.