The ending finale "Light". Things are not exactly perfect, and in a sense the part of the plot concerning the fraught relationships of the Goodman family aren't exactly resolved, Diana leaves Dan, Dan is in therapy with Doctor Madden and it's unclear if Gabe follows Diana further. Yet in the finale, the family acknowledges their past (at last) and decide to not dwell in bitterness but to look forward, and that there "will be light." They also all finally descend to the same level of the set, instead of Gabe usually being above them all or Natalie being somewhere in the middle. They're all on the bottom by the end of the song.
"Why Stay?/A Promise"; Dan renewing his promises to Diana from when they were young, and Henry making that promise to Natalie simultaneously.
Natalie freaking out that she could become like her mother if she enters a serious relationship with Henry, saying that she could end up his wife "sitting staring at walls, throwing shit down the stairs, freaking out at the mall, running nude down the street, bleeding out in the bath." He simply reassures her by saying that "crazy is perfect, and fucked up is perfect."
Even more heartwarming in the last performance by Adam Chanler-Berat and Jennifer Damiano when Adam Chanler-Berat can barely get out his lines because he is sobbing so hard. The orchestra is forced to wait for a long time for him to resume singing at one point, much to the amusement of the also-sobbing audience.
"Maybe (Next to Normal)" is a real tear-jerky example. It's the only time Natalie and Diana bond, and it's very touching.
Diana: We tried to give you a normal life...I realize now I have no clue what that is.
Natalie: I don't need a life that's normal. That's way too far away. But something next to normal would be OK. Yeah, something next to normal, that's the thing I'd like to try. Close enough to normal...to get by.
Diana: We'll get by...
Natalie: We'll get by.
The start of "Hey #3/Perfect For You (Reprise)" when the usually high "pretentious stoner-type" Henry comes on stage dressed for the prom in a frilly blue suit.
The moment in Next to Normal when Dan finally turns around and acknowledges the presence of the ghost of his dead son... which suddenly confuses the hell out of the audience, but that's okay since we're all close to tears anyway.
For this troper, it's when Dan says Gabriel's name which the audience has not heard before that point.
And when Natalie decides to go to the dance with Henry.
"You're like number four on my list of issues." "You keep a list?" "But you're my favorite problem."
Diana finally making progress to heal herself. Though it separates her from her family, you get the sense she's really going to be okay this time.
All of "Light":
Natalie: Day after day, give me clouds and rain and grey/Give me pain, if that's what's real/It's the price I'll pay to feel...