Since TV Tropes recently changed the trope to just Moments of Awesome because the things people added were so nebulously defined and pretty much ended up being "anything vaguely cool", I am going to use a strict definition here. As far as I'm concerned, a Crowning Moment of Awesome is defined first and foremost by being enormously satisfying. You don't just go "Heh, that was pretty awesome"; you go "OH HELL YES" and start to grin involuntarily. This usually happens when the character completely surpasses your expectations, rather than just being generally awesome.
I rather like 'I'm sorry, Professor; I must not tell lies.' from the movie version of Order of the Phoenix.
Speaking of Order of the Phoenix, one of my favorite moments is from the book, when the Ministry wizards come to arrest Dumbledore in his office:
Dumbledore said:
You seem to be labouring under the delusion that I am going to - what's the phrase? - come quietly. I am afraid I am not going to come quietly at all, Cornelius. I have absolutely no intention of being sent to Azkaban. I could break out, of course - but what a waste of time, and frankly I can think of a whole host of things I would rather be doing.
(Followed by Cornelius opening his mouth and closing it like a grounded fish and Dumbledore kicking a lot of ass and disappearing.)
Also, from the same book, Fred and George's escape. One of the most utterly satisfying moments of reading I have ever experienced. God, I love that book. I will never understand how it can be anybody's least favorite Harry Potter book.
As far as Crowning Moments of Awesome go in general, the one near the end of The Shawshank Redemption where you find out how brilliantly Andy escaped is one of the very most illustrative examples, simply because in a film where there are some pretty cool moments, suddenly there's this one montage that just utterly blows everything else away and makes your hair stand on end. It is amazing.
The bit in Avatar: The Last Airbender where Toph manages to
bend metal was unbelievably awesome. It's kind of game-breakingly overpowered and you don't give a damn because it is just so utterly
satisfying. "I AM THE GREATEST EARTHBENDER IN THE WORLD!" Yes, you are, Toph.
As for Gurren Lagann - there are plenty of pretty awesome moments, but thanks to the inherent over-the-topness of the series, most of them don't quite have that crowning feel - you
expect the characters to do something like this the whole time. That said, when Simon starts delivering inspirational speeches, he somehow manages to surpass my expectations anyway. You need a really special kind of awesomenes to stand there after the villains have explained why their position makes perfect sense, make an evolutionobabble speech about why humanity will through sheer force of will just defy the laws of the universe if that's what they have to do, and
actually succeed in convincing the viewer that you're right. Especially when that viewer is simultaneously going "aaa evolution does not work that way!" It murders my favorite scientific theory (including but not limited to: treating evolution as a mystical force emerging from the spiral shape of DNA that is completely analogous to the movement of a drill, treating humanity as the pinnacle of evolution, and treating the humanoid shape as being inherently more powerful than any other geometric form) and I don't care because it's just that awesome.