According to Captain James T. Kirk, the H-bomb was the ultimate weapon of the 20th century, and was described as a "doomsday machine": a weapon primarily built for bluff, never intended for actual use. The USSR (aka the "Reds") tested its first H-bomb in 1953, which made headlines in US newspapers. (TOS: "The Doomsday Machine"; DS9: "Far Beyond the Stars")
In 1968, as part of the nuclear arms race, an orbital H-bomb was launched by NASA, in the US, to counter a similar move by other powers on Earth. The sabotage and subsequent detonation of this suborbital warhead eventually led to a stronger international agreement to ban such orbital weapons. (TOS: "Assignment: Earth")
In 2267, the overload of the impulse engines of the USS Constellation resulted in a fusion explosion of 97.835 megatons. The detonation was used to destroy the planet killer. Kirk noted the similarity between the overload to that of an H-bomb detonation. He also noted that it was probably the first constructive use of such a weapon. (TOS: "The Doomsday Machine")
In a scene scripted, but not included in the final airing of TNG: "Contagion", the sabotage of the gateway complex on Iconia was said to have resulted in a detonation equivalent to a level 12 hydrogen explosion with a blast radius of nine hundred kilometers.  In the final scene of the episode the explosion was seen from orbit.
In The Making of Star Trek, the H-bomb was used as a comparison for the energy produced by a warp core. The difference between the two is comparable to the difference between lighting a match and nuclear energy. (p. 192)