When I say moments, I'm talking about brief sections. Maybe part of a scene, a short sequence, something like that. Just small moment that really stick out to you, have a strong effect on you.
In Flowers of Evil:
There's quite a few moments that I adore, but one that I watch over and over again is right at the end of the first episode
when Kasuga sees Saeki's bag and the ending them starts playing - just the robotic voice - and we hold on Kasuga's amazing expression, and then cut to the flower in full bloom, and then credits + the song's incredible instrumental comes in.
It sends shivers down my spine every time.
Aria the Origination:
In episode 9,
the moment when Athena removes both of Alice's gloves. It is the sweetest, most beautifully serene emotional thing ever dammit! I've seen it twice. Wept both times.
I'm just gonna list a bunch of random moments that come to mind. This list is not in order and certainly not anywhere near exhaustive (obviously).
End of Evangelion
That moment when
all the crosses go off on the entire globe. "I felt a great disturbance in the Force, as if millions of voices suddenly cried out in terror and were suddenly silenced. I fear something terrible has happened." That moment.
And of course, that moment when Shinji
rejects instrumentality and finds himself on the beach next
to Asuka.
Clannad: After Story
Episode 18: anyone who has seen the series knows which (two) moments I'm talking about.
K-On!
Episode 12:
encore during the school festival gig. It just makes me so happy.
Episode 20 (season 2): again, anyone who has seen this knows what I'm talking about. Didn't expect to hit me as hard as it did.
Legend of the Galactic Heroes
Episode 23:
Oberstein establishing himself as the ultimate conniving bastard by sending the probe to the planet that he knows is about to be nuked.
Episode 26:
the death of Kircheis. Apart from killing off a major character, which is always interesting to see if handled well (which they did), I love this moment primarily because its expected (and dreaded) impact on the development of Reinhard.
Episode 31:
that moment when Wenli is getting seriously pissed at the way he is treated by the corrupt politicians, and starts going on a rant alone in his room and writes his letter of resignation.
I haven't finished this series yet, but I'm sure there are many more great moments to come.
Ping Pong The Animation
Episode 11:
The photograph where you can see that Smile lost to Peco and got second place but is actually smiling again.
Hunter x Hunter (2011) (way too many great moments to mention, so I'm just limiting myself to two because I'm lazy and should be doing different things ffs)
Episode 50:
Gon and Killua getting caught by the Troupe after trailing Machi and Nobunaga. Despite knowing that there was no way that neither Gon nor Killua could be killed off that early (or at all), this scene made me almost shit my pants.
Episode 146:
Gon meeting his father. The moment the series has been building up to, and it was handled perfectly.
Might post more later, this thread is fun.
edit: God damn these are awful spoiler tags here on MAL, RYM does them so much better. Totally ruins my EoE joke (well, it was probably shit to begin with).
Prezbo, I totally agree with the End of Evangelion moment. That's one of my favorites as well. To add to the list:
Gunbuster
Episode 6:
Other than the entire episode,
the point where Noriko rips the drive out of Gunbuster and forces it into the black hole bomb, knowing full well the implications. She will never see anyone she loves ever again. Also, at the very end of the episode, with the transition from black-and-white to color. Beautiful.
Cowboy Bebop
So many moments. But
the final episode, where Spike looks at the camera and goes, "Bang." Up until the credits where you're gonna carry that weight. Absolutely crushing.
Revolutionary Girl Utena
Episode 29:
When Juri shatters the locket, representative of the love and hope she has for Shiori--and the realization that it will never come to pass. And at the end, where it's revealed Ruka wanted to free Juri of her complicated feelings for Shiori
Oh yeah, and the entirety of The Adolescence of Utena. What an insane movie.
Just a few. Some I can't remember off the top of my head:
Aria the Origination
Episode 9
Athena removes both of Alice's gloves, promoting her from Pair to Prima, giving her the title of Orange Princess. I cried. It was in this moment where I realized that Alice was indeed my favorite character.
Neon Genesis Evangelion
Episode 19
Unit 01 goes berserk, re-engages and defeats the Angel, and then tears apart and eats the Angel's corpse, absorbing its S² engine in the process.
Serial Experiments; Lain
Episode 13
Alice becomes traumatized, following Lain's attempt to protect her from Eiri. The scene where Lain is holding Alice's hands as Alice freaks out is one of the most affecting and disturbing scenes in anime. Not because of any specific imagery. Just the way it is conducted. It's the hardest scene in the show to watch, but ultimately the most important since it's the precise moment where Lain realizes that she has reached the point where there is no going back. That there is no fixing what she had done (at least to the point of putting things back to the way they were at the start of the series)
Cowboy Bebop
Episode 5
As cliche a pick as it is, I still love the scene where Spike falls out from the church window as the song "Green Bird" plays. One of the greatest examples of exceptional directing in anime ever.
Mushishi
Episode 12
After Ginko attempts to save Nui from the Ginko mushi, she protects him and turns the boy into Ginko as we know him. We also find that he does not remember Nui and only remembers the name Ginko. There are countless great scenes in this show however. My favorite episode was the 19th, String from the Sky.
Aria the Origination
Episode 13
Alice's retirement ceremony, where all the other undines participate. For such a relaxing series as a whole, it sure does have a heavy ending.