This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Blackest Night
Hal showing Barry a two page spread of all the heroes that have died since Barry was lost to the Speed Force, the longer you look at it, the more heroes you recognize, and the more heart breaking that it becomes. The most depressing parts are:
How the text describes that The Flash "finally sits down" as well as his heartbroken expression at discovering his friends Ralph Dibny (Elongated Man) and his wife Sue are dead as well (especially bad, because at that point we’ve seen both of them as Black Lanterns killing the Hawks.)
The fact that the Batman himself is at the center of the image.
Somewhat of a meta heart-warming moment that could do Saint Walker proud is that in the commentary, the artist says that they kept a full color version of the image, rather then just a green ring construct, “Just in case.”
This ties in to the finale as, after various heroes and villains are brought back to life, Barry looks around for Ralph and Sue but is told they're not there. You can see the heartbreak anew for Barry, that arch-enemies Captain Boomerang and Reverse-Flash returned from the dead but two of his best friends didn't.
Atrocitus kneeling in the dirt on a wasteland without life that was once his home planet. Even when this dialogue comes from the lips of what is essentially a demon, it will make you cry.
Atrocitus: This is what you did, Ganthet! What your androids did, Sayd! The Manhunters came... They came and we did... We did nothing to deserve this... We... We did nothing...
Especially noteworthy because up until this point, the comics have only shown Atrocitus as a violent, bloodthirsty lunatic, one with a sly, manipulative streak. This moment marks the first occasion we get to see him as a person, as he actually drops out of his Unstoppable Rage and shows that somewhere, somehow he is still the ordinary family man who lost everything because of a "programming glitch" he was before he joined the other Inversions. This single scene validates his entire vendetta against the Guardians for creating the Manhunters in the first place.
Bizarro deciding to protect Francine Langstrom from Black Lantern Solomon Grundy because she reminded him of Lois. Also:
When a Guardian is asked why he vowed to protect the Universe, his response: "I... I don't remember."
When Kyle Rayner tries to calm down Red Lantern Guy Gardner, Guy mistakenly declares him to be a Black Lantern, then tries to squash his head between a hammer and anvil.
Kilowog, Green Lantern drill sergeant, is surrounded by the corpses of Lantern rookies he feels he failed to save. And then they start rising as Black Lanterns, taking off to attack the Central Power Battery.
Kilowog: "Did you think YOU were special? That your names would never be enscribed in the Lantern crypt?!? You were all Lanterns! And Lanterns die... Lanterns die..."
Assuming that it is still canon even though it wasn't drawn, the death of the Rainbow Raiders. Seven random losers who stole the equipment of deceased Flash rogue, Rainbow Raider, the team saw Blackest Night as a sign of the apocalypse and drink poisoned Kool-Aid, Jonestown-style. Being D-list villains, the Black Rings don't even bother to resurrect them since none of the Flashes even knew who they were and as such, have no attachment to them. Your opinion may vary as to whether this is also an example of Black Comedy.
Okay, this isn't quite part of Blackest Night as it was of Infinite Crisis, but Booster Gold getting back in time to see himself attend Blue Beetle (Ted Kord)'s funeral and be unable to give an elegy to his buddy is pretty gutting.
Captain Cold versus his Black Lantern sister Golden Glider. He has to destroy what little love is left in his heart to defeat her, leaving him with a truly cold heart.
From Tales of the Corps, Saint Walker's backstory. It ends in a Moment of Heartwarming, but the death of his son is especially poignant. The narration merely reads "There is nothing more to say about that day."
Ring: WHAT DO YOU FIGHT FOR? A DELUSIONAL DEMAND FOR RESPECT. WILLPOWER. WHO DO YOU FEEL SYMPATHY FOR? YOU REGRET WHAT YOU DID TO LAURIE. COMPASSION. WHAT DO YOU WANT? EVERYONE TO LOVE YOU. AVARICE. WHO ARE YOU AFRAID OF? THE ONES YOU ONCE ADMIRED. FEAR.
Donna's baby. That entire segment. Especially when she crushes her own child's skull.
Proving Ice can always be more of a Woobie than she seems, in Green Lantern Corps issue 42, Black Lantern Ice attacks Guy (who didn't know about what had happened), and lays out a What the Hell, Hero? on him for barely giving her the time of day. Then, she pleads with Guy to kill her, because she can't take constantly dying and coming back. And remember, the rings use the thoughts and personalities of their hosts, rather than coming up with anything of their own. Meaning Ice has actually felt like that at some point. Oh, Tora...