This is a pretty spoiler heavy topic so everyone should use spoiler tags; just write the series name and the episode where it happens and spoiler the character's name.
Tengen Toppa Gurren Lagann:
Spoiler for episode 8:
Kamina's demise. It's a massive shock that permanently changes the direction and mood of the story. His death starts the series' transition from being a parody of Super Robot series to being a reconstruction of them.
In the previous episodes he appears to be the hero of the story with his charismatic personality and the fact that he's essentially the leader of the Gurren Brigade with the true protagonist Simon as his sidekick. His death also allows and forces Simon to step out from his shadow.
The way he dies is also quite memorable and a brilliant bit of mood whiplash. After snapping Simon out of his brief depression over Yoko choosing Kamina during the middle of battle, he is stabbed by Thymilph causing Simon, and probably many viewers (I know I did), to fall right back into depression. Then suddenly, he gets back up! He's alive! He's going to make it! And he teams up with Simon, gives an inspiring speech to Simon, and invents the series' iconic Giga Drill Breaker move and finishes off Thymilph. It's pretty much the most awesome he's ever done.
And then, he says "Farewell, comrades" or "Later, buddy" in the English dub and then dies for real.
