Joey using an approaching tank like a jumping ramp and galloping through the German lines before going into no man's land
The build-up to this one makes it even better. We see Joey backed into the corner and trying in vain to get out, as the tank keeps drawing closer and closer. Finally, he stands and faces it, and just when you think it's leading up to a Dying Moment of Awesome...he jumps over the whole thing. Wow.
The end of the film, where Albert rides Joey home once more
Anyone who's seen the stage play will agree that the phenomenal horse puppets are a Moment Of Awesome for everyone involved in their creation and control.
The reveal of the main Joey puppet. For the opening, the foal puppet is used, and the audience gets a while to get used to it. And then the music reaches a crescendo, the foal puppet is disassembled, and the huge horse puppet thunders onstage. That moment tends to get a lot of cheers.
Hell, they're awesome alright, but it might be good to mention that the play also has a huge (though of course largely hollow and skeletal) tank puppet/prop as well, which bursts through the obstacles of no-mans-land accompanied by smoke and darkness with flashes of light.