In "Pie-lette," the very first episode, Ned is about to touch Chuck for the second, final time and she asks, "Do you want to be my last kiss? First and last? Or is that weird?" He gently replies, "It's not weird. It's symmetrical."
Virtually any episode opening detailing the melancholy childhood of Ned, but especially the beginning of the Halloween episode, where Ned receives a postcard from his father saying he moved away then Ned going out in disguise to find him only to see that his father has moved on to a new life with new children.
The scene at the very beginning of "Dim Sum, Lose Sum": all those lonely little boys, playing roulette because they have nothing better to do. Since they don't have any money, they wager their most cherished possessions: a slinky, a toy car... all those intensely beloved treasures of childhood. (Ned wagers the last gift his mother ever gave him. And loses.) Because they're that desperate for some kind of connection with other people, some kind of bond with other children, even if it's not even friendship. And none of the adults notice or care, because they've all gone away for the weekend.
"Corpsicle." Chuck has learned that Ned accidentally killed her father when he was nine (he didn't know at the time he could only bring someone back for a minute or else someone else would die). At the end of the episode, she forgives him and then asks him to bring her father back to life for one minute. His reply: "No. I'm not going to bring him back just so you can watch me kill him again." By this point, everyone is in tears.
Also, Ned and Chuck's argument earlier in the episode.
Ned: Can't we keep the truth between you and me?
Chuck: It's hard to keep the truth between you and me when I can't look at you.
And then Ned falls apart....
Despite the craziness of the character just a moment earlier, when Olive said "I'm Tendering my resignation, and resigning my tender heart..." in the season two premiere. (And she swears that she hears music from some modern broadway musical playing somewhere every time she watches that scene.)
The way Ned teeters between awareness and unawareness of how broken he is. In particular, the scene in "Bzzzzz!" when Chuck asks him how long he'd lived alone and his answer—delivered, heartbreakingly, in his usual quiet monotone—is "Long enough."
Ned's description of his worst fear in "Robbing Hood," and what it says about how his mind works, and his relationship with his powers. Especially considering how vivid the idea clearly is to him. The fear he's been living with his entire life, with no one around even to reassure him, let alone tell him why he is the way he is or how to deal with it, is just horrible.
Ned: Ever since I was a kid, I'd have this dream where somebody would find out what I could do. It starts off with lots of ice cream and balloons, and ends in a small white room where little bits are cut out of me until there's nothing left to cut.