This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Nostalgia Chick
In the review of Grease, after failing to make over Nella, the Makeover Fairy starts to cry. While obviously played for comic effect, she sobs so hard that it really can make one feel sorry for her.
In Hocus Pocus, the Chick being close to tears when the movie makes her remember the kitty she had that got run over.
The Halloween costumes montage in the "Top Ten Villainesses". With the song and what we now know of her, it feels like reminiscing on happier times that she'll never get back.
In Thanks For Your Feedback, the terrified Death Glare the Chick gives Nella when the latter says she and Critic have a lot of common. The lady has issues, no question about that.
For all the shy nerds (male and female) out there, Critic looking like he's deep in self-loathing when he chickens out of holding the Chick's hand and she doesn't notice.
The hints in The Fifth Element, that she knows he's in love with her and is fundamentally pissed that he couldn't (or still can't) admit it to her, don't help.
The Chick's breakdown in Spooning With Spoony. While hammy and utterly hilarious, bear in mind that this was the first time we got to see her Broken Bird-ness. Up until that point, the most pathetic she got was the seriously awkward date with Critic.
It doesn't help that this breakdown happens when she's completely getting ignored while the rest are having fun. Spoony even asks why she's still there.
The brief moment of her mind obviously going back to the time when she was molested by her uncle, before coming back to a Slasher Smile-d "Merry Christmas!".
The Smurfette Principle is a bit more somber than most, detailing an important problem and her (the character obviously) dislike of her job shining through.
While the character of The Nostalgia Chick is nowhere to be seen, it'd still be a shame not to put "The A Word" - Lindsay's poignant look at abortion, including dealing with her own - on here.
Identifying with the daughters of the My Little Pony movie because her own mother always made her feel like crap.
Nella forgoing the Dance Party Ending of "Dreamworks vs. Disney" and going off to cry. And right after, we see Nella being completely ignored when she reads Chick a fortune while the latter reads something on her cell phone.
Nella sloping away like a beaten puppy when the Chick ignores her on the "nobody likes puns" thing.
The ending of the Thanks for the Feedback - We, Fit feature. Look at Nella as she obeys Chick's New Year's resolution command to do Chick's dishes for her.
Nella's death. Yes, it's taking the piss out of Kirk's Dropped a Bridge on Him end, but it's still Nella dying and the Chick actually showing emotion over it.
Before Dr. Tease comes in to the X-Men review, you'd be forgiven for thinking that the Chick was going to break down crying any second.
The Chick draping Nella's Star Trek shirt over the chair next to her (possibly out of regret for what caused the death in the place) and forgetting for a moment that she's not around anymore.
She snaps back almost instantly to claim she's happy about it, but she looks like she's going to throw up when she discovers Chicago is destroyed and Critic is dead.
Also serving as an awesome moment, the Sex Bot really letting the Chick and Dr. Tease have it for making him suicidal enough that he wants Dark Nella to destroy him. The fact that we never see him again after this makes it worse.
Chick's destroyed expression when she sees Dark Nella explode herself up. Contrary to what Lindsay says, she does have acting ability in her.
The last five minutes of the TLC video, where Lindsay gets out of character (she even takes her hair down) and is holding back tears as she discusses Left Eye's death, a murder of her friend at the time, and how it isn't right to make jokes about Amy Winehouse succumbing to alcoholism.
The Chick's Stalker with a Crush obsession over Todd doesn't get her a whole lot of sympathy, but you feel bad for her when she appears at Todd's place to announce she's over him and then instantly goes back to the "land of the lonely" when she gets it into her head she just needs to try harder.
The ending of "Channel Awesome Goes To Washington", where Lindsay is clearly exhausted, more cynical than ever about politics and very scared about what's going to happen to the livelihood of her and her friends.
She pulls as much dark comedy out of it as she can, but the Milo and Otis clips of the kitten(s) and pug getting hurt will make you want to cry if you're an animal lover.
Sliding into Nightmare Fuel when you see the pug fighting a bear. They did that. Like the Chick said, pugs are not built to fight (and they also have a lot of breathing issues from the flattened nose). And they have that fighting a bear.
Not to mention the fact that, apparently, at least 10 of the 30 kittens used in the "Milo falls off the cliff" scene died from that.
In Sister Act, Nella guilts the Chick by saying that she's not even getting paid for basically being her slave. If you remember Thanks For The Feedback II, that little bit is... disheartening.
The review itself and ending song is filled with laughs, but the scene in The Chipmunk Adventure where Chick and Critic talk about their site-given Distaff Counterpart roles has an odd Elephant in the Living Room feel of trying to avoid discussing a break-up. Not helped by how watery their eyes get. Much like in "Thanks for the Feedback", Critic accepting that he'll never have a BFF struck a chord with the lonely people out there.
During the Todd and Lindsay livestream, they discuss their lack of health care coverage. It's the saddest thing listening to them hoping that they don't get sick at all until 2014 (two years later) because they can't afford any medical bills.
Lindsay and Nella's vlog about The Host. Expecting a raucous good time of them trashing the movie? Well, instead you get both of them simply depressed and very subdued over how much the movie is probably going to hurt the prospects of us getting more sci-fi and fantasy films with female protagonists.
The comparison between 1996 and 2005 during the 'Independence Day / War of the Worlds review. It brought home to me in a way that I've never really seen so clearly articulated before how much better and hopeful the world seemed between the end of the Cold War and 9/11, compared to the shock, dread, and trauma of the first decade of the 21st Century.
Her documentary "The A Word," one of her most serious works, reveals that Lindsay had an abortion and feels conflicted about it (as she says again in her "Shut Up and Talk Interview"). Whatever your opinion on abortion is hardly matters because we don't even know what the situation was. Did Lindsay actually have a choice, or did some medical problem force her to abort? Did she make her decision with misinformation of some kind? Is it really all not that huge of a deal to her and we're just reading into it too much? We'll obviously never know.
The Loose Canon episode on 9/11. Unsurprisingly, Lindsay delves into heavy territory regarding a terror attack that claimed 3000 lives and set up many other wide-reaching and destructive events in the years following. It's made worse by the fact that Lindsay is a New Yorker herself and recently experienced a release of suppressed emotions she didn't even know she held back when visiting a museum about 9/11. It's not entirely mournful, but the tragedy of the attack definitely shows.
To really drive the point home, she closes the video by intercutting "La Vie Boheme" - in which characters loudly celebrate how hip and avant-garde they are - with Larry Kramer's enraged "We are in the middle of a fucking plague!" rant from the documentary How To Survive a Plague.
In her video on Guardians of the Galaxy Vol. 2, Lindsay talks about how this movie affected her, comparing the death of her own father with the death of Yondu.