This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Final Fantasy IX
The moment when the third Black Waltz massacred those poor Black Mages.
The look on Vivi's face when it happens is enough to break your heart, despite the fact that he's The Faceless and you can only see his eyes as he watches.
His body language in that scene thoroughly makes up for his lack of a face. Watching him press against the window as the mages fall, stumble backwards into Garnet's arms, or stand in front of the one hat on the railing is just heartbreaking.
The Black Mages suffer even more when Kuja gleefully admits that he tricked them into his service with the promise of lengthening their short lifespans, saying they're going to die soon and there's nothing they can do about it. The Black Mages have no choice but to accept their fate.
The moment where Queen Brahne dies on the beach outside her lifeboat. Yes, she might have gone mad with greed and killed thousands of innocent people, but that's still a young girl losing her mother and the only family she has left.
There's also the line where Vivi's narration says that he didn't feel sad at all, that he hated Brahne and wanted this to happen to her. And then he says "but then I saw Garnet cry".
Also the aftermath, including the destruction of Alexandria, giving Garnet a Heroic B.S.O.D. moment and causing her to go completely mute from the trauma.
The ending of her period of being mute was also a tear-inducing moment, but for the completely opposite reason.
And, yes, the moment when Zidane stays behind to be with Kuja in his final moments, who only just realized he had wasted his life and it had meaning just before he died. Like in the example above, Kuja is still Zidane's only real family, being his 'big brother'.
Not quite Zidane's only family. Which brings us to another tear jerker. Their little sister walking along one of the now dead Iifa tree's roots, telling Kuja that what he did was wrong, then thanking him for showing that the genomes weren't created for the wrong reason.
The final words of Vivi, saying goodbye to everyone and wishing they could have gone on more adventures. It's implied that he never lived long enough to see the reunion of Zidane and the others.
Vivi: Everyone... Thank you. Farewell. My memories will be part of the sky...
"How did you survive...?" "I didn't have a choice. I had to live. I wanted to come home to you. So... I sang your song. Our song." Oh goddammit. *sob* (qualifies also as a Heartwarming Moment). This is then immediately followed by the hauntingly beautifulMelodies of Life over the game credits. And did we mention that they also reshow key parts of the FMVs over the credits to jog your memory? Your stream of tears is now a gushing river of tears.
Beatrix's third victory becomes rather pyrrhic for her when she sees Garnet laying unconscious and in poor condition, prompting her to have a Heel Realization for all she had done and decides to pull off a Heel–Face Turn.
Even earlier than that, Beatrix becomes horrified upon finding out that she was used as Brahne's puppet while the queen plans on killing Garnet for treason.
One of the most well-remembered parts of the game, where Zidane's True Companions break him out of his Heroic B.S.O.D. after he discovers his true intended purpose as the 'angel of death' and the destroyer of Gaia, telling him that since he always believed in them, that means that they're going to believe in him too. All while the famous track of You're Not Alone plays.
Dagger: "You've always protected us. But you still don't understand that we looked out for you, too! We watched your back while you watched ours. And we believed in you the same way you believed in us! Just like you protected us... We want to protect you."
The destruction of Cleyra. There's something just plain wrong about destroying the home of what were essentially a bunch of peace-loving, nature-worshiping hippies.
A smaller Tear Jerker is near the end of the game, where you learn that Morrid, the Cool Old Guy who helped you earlier in the game and collected rare coffee, had died in an earthquake caused during the course of the game.
The destruction of Lindblum is the most devastating scene in the game. It's made even worse by the aftermath. Where any other form of media would have an implied holocaust or only talk about it, in FF9 you're forced to walk around a destroyed Lindblum, while the citizens give you short but horrific anecdotes about the attack and the Alexandrian soldiers waver between My God, What Have I Done? and bragging about their superiority. The stories include a little girl in the very first screen asking for her (absent, probably deceased) mother not to leave her alone, the synthesist's father having lost the use of his hands, the pickle selling woman having been blinded, and that's only three out of dozens of potential conversations. The entire Industrial District was wiped out. Just think about how many people that would be and what that means.
A rare one for the enemy side, but Kuja learning that he's going to die soon, and the cackling fear in his speech when he realizes that Garland isn't lying about it, causing one of the most triumphant and saddening examples of the Villainous Breakdown I've ever seen.
"Freya, you say? I believe this is the first time we have met..." Ouch. Followed by Vivi's innocent, "What's the matter, Freya? Are you crying?"
(during Kitchen ATE) "Grandpa... I don't want to be alone anymore... Help me do this right."
The black mages' understanding of death, or, as they call it, "stopping."
"One day, Mr. 36 stopped moving. My friend who knows a lot of things says that this is what "death" was, and that we had to bury him. Mr. 36 is buried under the ground now, but I don't understand why. He's going to come out again one day, right? When he does, I'm going to wash him off in the pond."
Mr. 288 explaining what a cemetery was for to Mikoto gets me teary every time:
"...You're right, but I don't think we build cemeteries for the dead. Sure, it may seem pointless to you, but... How can I describe it? It's so that we can think like this: 'We'll never forget you. We'll remember you every time we stand at your grave. And we won't let the fear of death, which each of us knows, stop us from living our lives. ...Because my friends will remember me when I'm here.'"
Coupled with Harsher in Hindsight in an optional little scene after Alexandria gets destroyed in disk 3. If Zidane goes up to the place where he had previously found Garnet singing in Lindblum, he'll find her again and try to talk to her. At this point the player doesn't know that Garnet has lost her voice. He continues to try and make conversation, growing even more worried as she doesn't answer him. He leaves thinking he's offended her and we see a thought bubble showing what Garnet is really thinking:
Garnet: (thinking) Zidane, you're so sweet. Thank you.
Zidane: I had a whole speech ready for her. But it would've been a lie! How could I lie to her!? 'Good luck, Dagger! I'll be watching you from afar. Come find me if you need someone to talk to.' It's a big fat lie! That's not how I feel at all! That's not how I feel... at all.
There's a sidequest on Disk 4 where the player will eventually discover a message written on the Eidolon Wall in Madain Sari - from Garnet's birth father. He wrote it after the attack by the Invincible and was badly wounded - so he's writing it knowing he will die soon, in the hope that his wife and daughter will read it. Even sadder with the knowledge that Garnet probably will never know his name or remember what he looks like.
"I survived the storm. I wonder if you two are okay? I see the two of you smile every time I close my eyes. I imagine I see you when I open my eyes. I have a mortal wound. I won't be able to wait for you very long. I regret being so unemotional all these years. I'm writing down everything here in the hope that you'll read it someday. To my dearest wife, Jane, Although we fought many times, and I may not have shown my affection enough, I love you very much. To my beloved daughter, Sarah, My life changed when you were born. You made me happy. These are the things I want you to know."
Two more messages can be found on the Eidolon Wall, these two directed at Eiko. Even those who survived the initial attack ultimately did not last long, and as they were dying, they were well aware of what it meant for the last Summoner to be born.
"Eiko. You are a treasure born to a dying village. We are dying, and there is little we can do for you. We will return to the stars with one wish in mind. If legends are not born of Eidolons, and eidolons but born out of legends, let us leave this place with one wish: if we can give birth to a legend, it shall create an Eidolon that is a friend and protector of humans."
"Eiko, my lovely child. Until you turn 16 and have your own Eidolon to your control, stay in this village. Then build strong friendships with others. I wish for your happiness from far away."