But most Godzilla movies features humans trying to control, redirect, contain, or fight Godzilla, only to fail in the attempt.
One of the few redeeming features of the mediocre second movie, Godzilla Raids Again, is the way it focuses on the citizens of Japan just trying to adjust to life in a reality where the risk of Godzilla attack is just part of the status quo, like the risk of an earthquake or typhoon. It's more about coping with the unavoidable than it is about defeating the monster (although they do find a way to defeat him at the end). But it fits with the experience of the Japanese people, who've always had to contend with one natural disaster after another. I used to think that Japanese movies' and cartoons' preoccupation with mass destruction was a legacy of WWII, but I now understand that it's a much older fact of life there, given the constant blows that their own environment have subjected them to. It's not by chance that Godzilla comes from the sea, or that Rodan and Mothra destroy with hurricane-force winds.
As for Godzilla's motives for his actions, they vary from film to film. Let's see... The original said he was displaced from his normal feeding grounds and wandering in search of a new food source, so yeah, I'd say he was there to devour people. Raids Again, conversely, claimed that he attacked Tokyo because he was both drawn to and infuriated by the lights of the city (so they were able to draw him away from populated areas using flares). In many later movies, he was drawn to the other featured kaiju, seeking to battle them. Eventually he became the hero of the franchise and acted to defend his territory (i.e. Earth). In the '84 reboot, it was established that he fed on nuclear energy and was drawn to reactors; G vs. Megaguirus expanded this to include any high-energy source. I believe that in the '90s Mechagodzilla film, he was drawn by the cries of the baby Godzillasaurus. In GMK, he was a supernatural force of vengeance, possessed by the souls of the wronged dead of WWII and driven to exact retribution for the crimes of Imperial Japan. In the Millennium-era Mechagodzilla duology, he was drawn spiritually by the bones of the original Godzilla, around which Mechagodzilla had been built. But in Godzilla 2000 and Final Wars, I think, he was basically just a force of pure destruction.