In Godzilla Final Wars, the scene in New York City between the pimp, the homeless drunk guy, and the cop.
Captain Gordon in Final Wars gets a particularly dry one. At one point, he orders the civilians to get to their ship, while he holds off two aliens. They end up getting pinned down by a huge number of the aliens, who only are defeated when the head alien sets off the self destruct on the ship. Gordon, fresh from his own battle, just saunters past, ignoring the carnage, and in an irritated voice says, "I though I told you to get to the ship" and keeps on walking, katana on his shoulder.
Gordon had a good one during his fight scene as well. One of his opponents was female, and after he gets the upper hand, he has his fist pulled back ready to deck her, when she gives the old "you wouldn't hit a woman would you?" routine. He hesitates, opens his hand, smiles...then says "Yeah." and knocks her out with a karate chop to the neck!
This is more mildly amusing: Godzilla walks off, and Minilla runs behind, as if to say "Hey, wait for me!"
The first turning point in the end clash of King Kong vs. Godzilla, which is Kong making a dash at Godzilla... only for him to step aside, causing Kong to slam his face into a rock, then pass out. By this time, the creators were aware of the inherited goofiness of kaiju movies, so they intentionally hammed this film up. The fact that the suitsnever stop looking like suits then adds an unintentional layer of hilarity to the scene.
In Godzilla Final Wars, Godzilla is fighting King Ceasar, Rodan, and Anguirus. Anguirus, in rolling death ball form, charges Godzilla, who swats him away with his tail toward King Ceasar. King Ceasar responds by performing a soccer kick and sending Anguirus back toward Godzilla, though missing. Godzilla proceeds to... try and intercept Anguirus like a goal keeper, though he fails.
In the Dark Horse Comics one-shot Godzilla Color Special, when G-Force is trying to get a town of villagers to safety Kino asks why they've stopped... and then sees the reason.