Daria/Tear Jerker

Helen's Break the Cutie moment in 'Psycho Therapy': "Everybody hates me." Much Daria Fan Fiction is devoted to this. Just look for the words 'Angst Lords' on the Daria Wiki.
At the end of Lane Miserables, just as it seems as if Daria's crush on Trent will finally die, Trent remarks that if Daria were a little older, he'd consider going out with her. As he leaves, Daria daydreams a happy end with her and Trent. Daria snaps back to reality, muttering "Damn..." under her breath.
There's also Quinn's speech on why being popular and pretty is so important to her in "Monster".
In the episode where Quinn becomes obsessed with what she believes is her guardian angel, she has a crisis of faith and asks Daria for advice. Daria takes the blunt tactic of simply stating that until proven otherwise, she doesn't believe in any afterlife. Something about the way Quinn says "But... that's so sad..." is just heartbreaking.
When Quinn's tutor rejected her and she began to cry in Daria's room.
Boxing Daria, the entire episode. It's basically, the sight of an over-sized refrigerator box causes Daria to recall parts of a childhood memory of her in bed, overhearing an argument between her parents and her dad storming out. This memory keeps nagging at Daria and leaves a real strain on her, until she finally remembers what the argument was about. Jake and Helen were fighting about her, due to the collective stress of working aggravating jobs and being called in by the school because Daria wouldn't socialize with the other kids. The box was important because Daria had one just like it when she was younger that was a sort-of haven. It's just the entire episode has Daria on the defensive and very insecure, seeing her be that emotionally vulnerable without bursting into tears and thinking that she's a cause of constant and unwarranted stress on her parents and family because she chooses not to socialize and "be herself". This is something that just about everyone has gone through in their life, and it's hard not to sympathize with Daria and be a little awed by her when you realize she began to reconsider the decisions she's made and wonder if she made them wrong. Awed in seeing her show that much humility by admitting she may have been wrong.
The end of "Dye! Dye! My Darling". After "The Kiss", Jane tells Daria that she and Tom broke up, and then they argue about the events leading up to that point. At the end, they note they are the kind of friends who can't stand to see each other.
Jane during most of Is It Fall Yet? She broke up with her cheating boyfriend, has cast off her backstabbing best friend, and only has her narcoleptic brother to comfort her. She tries to retreat to an art colony in the middle of nowhere to clear her mind, and has one of the other artists try to get her drunk and into bed. Someone give this girl a hug!
There's something incredibly tear jerking about Kevin and Brittany's implied separation in Is It College Yet?, probably due to the fact that out of all the relationships in the show, theirs were always the closest and the happiest.
- Closest? They've broken up multiple times, regardless that they get back together, lack any qualms about cheating on one another when they're separated, and in College Bored we're shown their college fantasies, where they've each given each other the respective heave ho.
In See Jane Run, Jane joins the track team and becomes a big athletic star. Daria talking to herself is funny until it hits you that she's doing it to compensate for Jane being busy with practice all the time. Jane is her only real friend in the world, and not seeing her really takes its toll on Daria.
In Is It Fall Yet? Daria has finally made a bond with the outcast boy at the summer camp she is volunteering at. He starts to open up to her, so that she can help him...and O'Neil comes waltzing up and interrupts, making Daria's attempts at friendship sound more like manipulation. Incensed, Link storms off, followed by Daria, both looking like they want to cry at how everything went wrong in a matter of seconds.