Godzilla killing the American Zilla in less then twenty seconds is flat AWESOME. Adding "We're All To Blame" in the background is icing on the cake.
Hell, the whole montage of Godzilla walking around owning every monster that he comes across is awesome, especially when you consider that the monsters have all single-handily overwhelmed Earth's defenses. "Last resort" indeed.
For fans of Zilla, seeing him in a japanese Godzilla movie at all is pretty awesome.
The mutant soldiers taking down Ebirah is one of the few times humans actually take down a kaiju, and it is awesome.
Ozaki single handedly kicking the ass of the new controller.
King Caesar, Anguirus and Rodan versus Godzilla. Even if they lost, they held him up longer than anyone else apart from Monster X. That takes some serious balls.
Might damper the Awesome a bit but could cross into heartwarming as there might be a REASON why they held out longer. Godzilla didn't want to truly kill his friends.
Godzilla killing Gigan even though not in continuity with Showa it was satisfying seeing something of an end to a monster that fled away in two films with no conclusion. Fulfilled again by Mothra later in the film.
Godzilla's reawakening is one of the most epic moments in the whole franchise, especially with the flames burning in his eyes.