The entirety of Operation Yashima in 1.0. The movie took what is one of the most boring fights from the series and made it so mind-numbingly epic that the entire movie is worth watching for this scene alone.
2.0 is full of moments where you go "Wait, it's only been X minutes, and there's 118-X minutes left of this!?".
Asuka's introductory fight, where she destroys an Angel after being dropped out of a plane and kicking it through the core before she hits the ground.
Or if you're watching the dub, "Invert Controls. Backdoor code. THE BEAST!"
Shinji is like a panda in this brave new world. What do pandas do? They look sad — right up until you piss them off, and they start shooting Frickin' Laser Beams out of their eyes, and rip you apart with their bare hands! Do not make Shinji a sad panda. You wouldn't like him when he's a sad panda. (See Big Damn Heroes.)
"Give Ayanami...! BACK TO ME!" At this point, the fandom officially stopped making fun of Shinji.
It's even cooler in the dub. Shinji says (in a really creepy, harsh voice): "I want Rei. Give her back!"
The moment just before Unit 01's ascension to godhood, the exchange between Shinji and Rei:
Rei: "It's fine, Ikari-kun. Even if I disappear, I'll be replaced. I'll be replaced."
Shinji: "You're wrong! There's no other Ayanami but you! That's why I'll definitely save you!"
Shinji just reaffirmed Rei's worth as a person and declared that he would save her even if he has no idea how to do so. For all intents and purposes, he just told the outlook of the television seriesto suck it. That is awesome beyond measure.
Kaworu appearing at the end with Unit-06 and the Not-Lance of Longinus to stop Shinji/Unit-01 from ascending to godhood at SAVE THE WORLD...which, given his role in the original series, is beautifully ironic.
The second teaser for 3.0. EVAs IN SPAAAAAAAAAAAAAAAAAACE!!!
After an enthusiastic and futile solo assault, somehow managing to revive a mangled Unit-2 for long enough to help Rei and Unit-0 get through Zeruel's AT Field. (Rei throwing Mari back and thanking the pilot she'd never met with what may have been her last breath is awesome in another way.)
And, apart from the aforementioned Za Beasto moment, her finding Shinji and telling him, in so many words, to sackup and stop feeling sorry for himself.
