"THE EMPEROR PROTECTS!", or anytime Shinji's imaginary friends save him from his self-doubt. Some of the Maya-Ritsuko moments (not those kind) are "awwww"-worthy, too. There's also the scene between Rei and Shinji in the Alternate Universe omake, which is so cute that it gives Asuka a nosebleed.
Shinji earning Rei's eternal devotion at the end of the battle with Ramiel. Also insanelyawesome, and gives Ritsuko a headache trying to figure out how they managed it.
Shinji and Asuka's conversation in chapter 36. It starts out with Shinji trying to cheer Asuka up, and it ends up with Shinji growling "You. Are. Mine" in her ear, kissing her, and Asuka tackling him and declaring "And YOU are MINE, Third Child."
Shinji training Asuka to use her A T Field in chapter 22.