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Tear Jerker: AKIRA
The death of Yamagata. Damn... he thought he had the upper hand against Tetsuo.
There's the death of poor Takashi, which happens right when it seems things may start getting better and as he happily goes towards Akira, calling out to him and asking if he remembers him from the past. And right when he's extending his hands to touch the kid he's so happy to see again... BANG, courtesy of Nezu. No wonder Akira has a terrible Heroic BSOD as he sees Takashi die, completely loses control of his powers, pretty much blows up the whole Tokyo by himself.
Then there is the death of Kaori. She had zero to do with his condition. On the contrary, she loves him and genuinely cares for him, despite him being a royal prick. Yet, she pays the ultimate price.
Made even worse in the manga, where she's shot to death by Tetsuo's aide and dies in Tetsuo's arms.
When the Colonel is reintroduced in the second half of the story, one of his former soldiers recognizes him and salutes to him. The Colonel dismisses him, as he cannot help anymore.
Takashi's and Kaori's deaths.
Although, in the latter's case, viewers might be a bit too... distracted to feel sad.
The manga version of Kaori's death is very different than in the movie, and is more tragic than horrific.
The death of Sakaki; Lady Miyako spends the rest of the manga grieving for her death.
The moment Kei and Kaneda see each other again after the latter is presumed dead. The whole thing is eventually foiled by Kaisuke
The moment when Kei offers herself to Kaneda, which he finds very odd considering the situation; Kaneda furiously lashes at Kei after learning that Kei would act as a medium for the Espers and Miyako to combat Tetsuo, and that Kei was offering herself to him in an expression of farewell. Kaneda intends to leave Miyako's temple to raise battle against Tetsuo to keep Kei from doing so; Kei is about to be left completely heartbroken, given that her offering was actually sincere and utterly rejected, when Kaneda suddenly rushes back to lovingly kiss her goodbye.
Not including that Kei's expression of joy after he leaves... it speaks volumes of how much he has come to love her; she was about to be left thinking that her love was one-sided. If there were such things as thought bubbles in the manga, she would be thinking "Gee, what d'you know... that's MY MAN going to battle for me!"
Exacerbated by the fact that she thought Kaneda was about to leave under the impression that Kei thought so little of him, given that she didn't consider his feelings in making the decision (an additional reason why he might have reacted so angrily towards her).
This doesn't keep her from fighting, though.
Kaneda's confession of friendly love towards Tetsuo at the climax, revealing that Tetsuo's impression of him was disastrously skewed. ''I just wanted to be your friend" 
When the Espers reveal to Kaneda why they allowed themselves to be subjected to such horrid experimentation, it reaaaaaly makes you wonder whether you have friends that love you like that.
Not mentioning that they look so happy that it literally hurts.
When Kaneda reestablishes the Tokyo Empire at the end of the manga, the gang rides to the horizon with Kaneda on front and center with Kei embracing him on his back; to his left, the spirit of Yamagata rides his chopper; to his right, the spirit of Tetsuo rides as well... and then the ruins of the city start reconstructing themselves. These young people might have a future after all. It doesn't get better than that!
On a more subtle note: when Tetsuo transforms into another universe, we hear him proclaim his own name in a worried and reluctant manner. There's something quite sad about this.