Godzilla is much more than just a movie or two. Godzilla is an enduring culture legend, as well as the most recognizable Japanese cultural symbol. He first appeared in 1954 within the Japanese movie of the name, and possesses starred in various movies, comic books, animated shows, and more. He even has a hit rock song about him, "Godzilla" by Blue Oyster Cult. - Godzilla 2014
His origin stories vary somewhat, however they all include atomic mutation and since the Atomic bombings of Wwii remained as fresh in the minds with the Japanese during those times, he's seen as an metaphor from the perils associated with weapons of mass destruction. Some follow on movie stress the possible risks with pollution too.
Although he started being a monster, seemingly unhappy and bent on destruction and definitely terrifying, some later roles showed him like a hero, often protecting Tokyo off their monsters and customarily playing the "good guy." In later movies he's gone onto be described as a villain again, but is portrayed as much more intelligent and feeling. He even adopts a son in one movie, named Minilla. Minilla went on to many other movies also.
Godzilla has won several awards including Best Supporting Actor ("Godzilla vs. Mothra), several Japanese Oscars, and he has their own star about the Hollywood Walk of Fame. - Godzilla 2014