A nuclear missile was a weapon consisting of a programmable guided rocket craft used to carry a nuclear bomb.
In 1968, Gary Seven sabotaged a nuclear missile. (TOS: "Assignment: Earth")
Three hundred years later, the Ekosian Nazis attacked the USS Enterprise with a nuclear missile. (TOS: "Patterns of Force")
The first Earth warp vessel, the Phoenix, was constructed out of an old nuclear missile and used a nuclear missile silo as its launch point. (Star Trek: First Contact)
According to Spock, the Earth-Romulan War was fought with primitive atomic weapons by 2266 standards.(TOS: "Balance of Terror")