This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Grey's Anatomy
Cristina crying in Owen's arms over the death of her father.
Everyone's faces after Meredith drowns and almost dies. Derek and Cristina especially are inconsolable.
Any time we see Owen with kids is this for a little while. He really wants and loves kids but is in love with Cristina who doesn't and aborted their child. It eventually leads to them breaking up (multiple times). This is a tearjerker in and of itself because they love each other so much but want different things out of life.
Izzie breaking down crying when Denny dies.
Izzie's famous "What about me?" speech to Denny when she tells him of her plan to cut his LVAD wire so that he will qualify for the heart transplant.
The season five finale: Meredith realizing that John Doe is George, Izzie flatlining in Alex's arms and then meeting George in the elevator, dressed in his army uniform.
Dark Was The Night, an unrelentingly bleak episode in which everything that can go wrong does.
This happens in the season eight finale, "Flight".
If you have grown up around or known alcoholics, Lexie's rant to Meredith in 4.08 is heartbreaking.
Lexie: Everyday is my mothers birthday. My mother was born in March. He lied. He's a liar. And I'm glad. Really, I'm glad that you found him charming. I'm sure he was delightful. He's a blast after five drinks, not so much after nine though; he gets a little weepy and mean. He's a drunk, Meredith. He probably came in and told you how wonderful you are. How sad he is he doesn't get to spend more time with you. You know, yesterday he told me I was his favorite daughter. The day before, I was an ungrateful bitch. The week before, he wrote me a check for $20,000 because he said I deserved everything life had to offer, because he was so proud of me, a lifetime's worth of proud. So thank you for letting me know that I need to keep a better eye on him. Thanks.
In season 9 there's an episode of a liver transplant patient. The patient, who is gay, had been waiting for a liver for so long that he was still married to a woman when he got sick. He and his husband are excited, talking about wanting to spend 30 additional years together to make up for lost time, since it took him such a long time to come out. The patient does finally get the liver, but his body rejects it, and he and his husband only have a few days left together. An intern starts crying and even Cristina looks sad.
Another episode has two single parents, both with newborns in the ICU, bond over the shared experience and become each others' close friend/confidant and support system. The woman has been waiting for a heart transplant for her daughter for a long time, while the man's son seems to be doing better. Then the boy starts to get a lot worse, just as the hospital has a heart available, and he bypasses the girl, who is at the top of the list. This causes a rift between the two - the mother is appalled by this revelation and immediately distances herself from the other parent who is overcome with guilt. At the end, they are still upset but the woman tries to be happy for the guy instead of being angry.
The death of Dr. Thomas, which sends Cristina right back to Seattle Grace.
The aftermath of season 8's plane crash: Every scene from the first few episodes of season 9 of Callie and Arizona, the days leading up to Mark's death and him waking up just to end up knowing he will be dying soon, the Cristina and Owen scenes, etc.
The actual plane crash episode when Lexie tells Mark she loves him as she is dying.
Richard leaves his ailing wife's side and attends Bailey's wedding. Why? Because Adele died. The last shot of the episode is an Imagine Spot of her and Richard dancing at their own wedding.
When Richard sings that song "My Funny Valentine" to his wife, Adele who's Altzheimer's is getting worse and he's trying to bring her out of her delusion.
Also, the same song plays when Richard sees that glimpse of Adele and him dancing at their wedding. So heartbreaking!
Season 8 has an episode in which Morgan, one of Alex's interns, gives birth prematurely. The baby has a ton of health problems and the father spends the whole time complaining about how he's missing work (he worked at a different hospital) and not wanting to be there for his sick child. Morgan gives the father an out, and he doesn't hesitate to walk out on his girlfriend and newborn son by the end of the episode. Morgan starts to lean on Alex for support but ends up falling for him, which causes him to keep his distance. Then the baby eventually dies a few episodes later.
"Damage Case" (season 2). A family is hit in a car accident by an intern from another hospital (played by John Cho). At first it seems that the family is fine and that they're mostly just for laughs while the real medical issues are with Cho's character. However, this assumption is turned on its head when one family member's catastrophic injuries are revealed while Cho's character was merely tired. The tears really get jerked when Cho apologizes to the father for killing his pregnant daughter.
"Into You Like a Train", in which a man and a young woman were both impaled on a pole during a train crash. Their injuries are such that the only way to operate is to pull the woman backwards off of the pole, most likely sentencing her to bleed out, and then operate around the pole and hopefully get it out of the man without making his injuries worse. The man survives, but the woman (Bonnie) does die, and her tearful but calm acceptance of her own impending death is absolutely heartbreaking. Even Derek needs a moment to compose himself after breaking the news to Bonnie's fiance.
The season nine finale has two tearjerker events that double as Heartwarming or Badass.
When Meredith goes into labour, she's informed that she needs surgery because of her son's dangerous position in the womb. After a few tense moments the baby's delivered and Derek goes to PEDS with him to make sure he's ok. It's only after all the senior surgeons leave the room that it's discovered Meredith's bleeding internally from an earlier fall. She's forced to direct the interns how to operate on herself before passing out, despite being clearly terrified. Bailey, Derek and Cristina's reactions are all various forms of sad as well.
After a bus goes on fire in the hospital parking, Jackson is the only one who realizes that a little girl is still trapped. Everyone notices the missing pair right as the bus blows leaving the mother, Hunt and Callie horrified and April completely devastated and heartbroken. Just as everyone's convinced Jackson's dead he walks out of the fire - with relatively minor injuries from an explosion - with the little girl safe in his arms. April is not the only one to break down in tears during the whole event.
Especially, in "Disarm", when the local college is shot up and it brings back memories of the hospital's own trauma from the Season 6 finale. Also that scene where the students sing their school's alma mater. Absolutely chilling.
Also, Jackson comforting the mother of the shooter is a Heartwarming moment. It takes real compassion to comfort someone that many people think wouldn't deserve it.
Season 11, episode 5: after 30 days during which Calliope and Arizona took a "break", with Arizona needing some space and Calliope trying her hardest to keep her mariage together, they meet again before their therapist. Arizona realizes that she needs Calliope more than she knew, calling her her anchor, and tells her she wants to spend her life with her. Calliope, on the other hand, breaks down in tears, and says to her that she realized that by trying to keep her mariage together so hard, she ended up feeling stuck and not being happy, and that at this point she considers the situation unsalvageable, wanting to finally being able to love herself instead of trying to love Arizona so much. She was finally happy during the break: going back to Arizona would mean losing herself once again.
Season 11, episode 11: April and Jackson have found out their baby has osteogenesis imperfecta, meaning that he'll die very soon after birth. They have to decide what to do and eventually deliver the baby and hold him until he dies a few minutes later. The entire situation is especially hard for Amelia, who went through a similar situation years earlier. Do not watch Grey's if you're pregnant.
Season 11, "How to Save a Life": Derek's death and Meredith's reaction. Just before she gives the okay to remove life support, she has several flashbacks to the most important moments in their relationship. Then she tells him that it's okay to go and that they will be fine. The cover of Chasing Cars used during that scene made it even more heartbreaking.
When Mark's daughter gives birth and Mark is holding his grandson and he has to give it to the adopting parents.