This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Nausicań of the Valley of the Wind
Nausicaä of the Valley of the Wind is a story about life (but mostly death) in a post-apocalyptic wasteland. It's only natural that things get very sad very quickly.
The treatment of the baby Ohmu gets this devout insect-lover wibbling like crazy. The humans capture it, spear it all over, and drag it through the air, squealing pathetically and bleeding, as bait to draw out the parents, because Humans Are Bastards. Sure, everything turns out okay in the end, but the moment is definitely there.
When Nausicaä tries to keep the baby Ohm from moving and her foot hits the acid lakeů let's just say that it is hard to forget her heroic pleading screams. Pass the tissue please.
Nausicaä talking to Lord Yupa in her plant chamber about how she discovered that it isn't the plants of the Sea Of Corruption that are poisonous; it's the soil they grow in. She then goes on to say that as there is no point in continuing her experiments, she has shut off the water supply. She explains all of this very calmly, but then breaks down in Yupa's arms.
Lastelle's death at the beginning. Nausicaä does everything in her power to save this girl she barely knows, but once she catches sight of the wound in Lastelle's chest, she knows there's nothing to do but hear her final words and let her die in peace.
Later when Nausicaä meets Asbel after they find themselves beneath the jungle; Asbel reveals that Lastelle was his sister and regrets not being there in her last moments.
When Nausicaä is explaining her science experiments to Yupa, she says that she was looking for a way to cure her father's sickness (brought on by decades of too much time around the Toxic Jungle), but as he was assassinated by the Tolmekians, all of her efforts had been in vain.
That scene of Nausicaä and the baby Ohmu at the acid lake mentioned above has an additional bit of heartbreak in the movie ľ Nausicaä had already been shot in the foot. That means some of the acid got inside her woundů
Nausicaa's death in the film. She is ultimately revived by the Ohmu who are profoundly moved by her effort to return them their child, but the dead silence followed by the mass of grieving that comes when everybody realizes she was indeed dead is still overwhelming. Even more so as the baby Ohmu and Teto both mourn over her body with the now calm herd.
If the 1984 dub did anything right, the voice actress of Queen Selana, Linda Gary, managed to convey her pain and Captain Ahab tendencies regarding the Ohmu. She was in the wrong, but Gary made her sympathetic enough to understand her point of view.
Nausicaä admitting to Yupa that she does not want to go to war and only agreed out of a sense of duty to her ailing father. Her being away for an indeterminate period of time is why she shut down her science experiment.
The death of the Holy Priest of the Mani Tribe. Sure, he goes out with his proverbial middle finger extended to his former superiors and protects Nausicaä from evil (all badass as hell), but this is a guy who has led his people since before most of them were even alive. His final words were telepathically screaming to Nausicaä, "You must not come [to help me]!!"
Poor Ketcha seemed particularly close to him, and suffers something of a Heroic B.S.O.D. once he's gone ľ to be fair, she was standing right next to him when he ripped off his gas-mask in the middle of the rotwood and got stabbed by over a dozen bayonets.
Pretty much everything that happens to Kushana.
Her own half-brothers sold her out to the Doroks because they feared her charismatic power, so she got to watch as her own men were slaughtered. Twice.
We learn in a flashback that when she was a child, her step-father the Vai Emperor tried to assassinate her via poisoned wine. Her mother took the drink in her placeů and the poison literally rotted her brain. Shortly before leaving for the front, Kushana tried to speak to her one last time, only to find she'd replaced her in her mind with a baby doll.
In the oasis where Nausicaä meets Chikuku, she communes with the last surviving monk ľ whose philosophy is noticeably more nihilistic than the Mani tribe's Holy One ľ and enjoys the peaceful bliss of the areaů when all of a sudden the place begins to be overwhelmed by miasma. She runs to the temple to warn the monk, only to find he has died (and might have actually been dead for a long time).
As the third Daikaisho gets underway, Nausicaä has had enough trauma for one lifetime. She finds the dead Ohmu scout and climbs atop it, declaring that she will become Forest with them. She would have died right then and there if the Ohmu weren't determined to keep her alive.
When Nausicaä takes a spiritual journey to the birthplace of the Sea of Corruption to discover that that area has been purified and restored to its pre-human state, and she realizes that (1) the air is so pure that it may as well be poison to modern people, and (2) mankind is not worthy of experiencing it.
In-universe example. Late in the manga, we are introduced to Tepa, a little girl who was Nausicaä's protegé. On the day Tepa becomes a windrider ľ normally a cause for celebration ľ everyone in the castle is morose (and not just because of a Dorok ship landing nearby). Obaba sums it up: "I know what you're thinking; you think that the birth of a new windrider means the old one will never return to the Valley."
Teto's death and burial.
Lord Yupa sacrificing himself to protect Kushana. He smothers a grenade in his cloak, and even though he doesn't flinch when it blows his arm off, at that moment you realize he's a goner. Sure enough, he dies shortly thereafter, but he makes sure to go out in spectacular badass fashion ľ protecting Kushana from a melee attack.
Ohma's death in the manga. "I'm unsure, mother. Have I become a good person?"
The final page of the manga where it's heavily implied that Nausicaä never returned to the Valley. Or if she did, it wasn't for long.