This begins right after Naruto and Sasuke's confrontation in episode 134, as Sasuke stares down at his unconscious rival, and continues as he stumbles off to Orochimaru while Kakashi starts hauling Naruto home.
Most of the time it rains when something bad happens to the Uchiha. It rained for Itachi back when we thought he was the Big Bad and during his and Sasuke's fight.
It also rained when the Third Hokage died and when Asuma died. There'a also a perpetual Gray Rain of Depression over the Hidden Rain Village; one of the characters even compares it to the country constantly crying.
The final dramatic climax of the Fruits Basket anime occurs in the rain, after the rest of it is sunny.
Occurs in Gankutsuou. Most often in the later half of the series. Albert even walks home in the rain in a depressed manner at one point.
This happens in the 25th episode of Death Note, which has an unusually poetic kick to it overall. At a moment of high drama, it instantly becomes Dramatic Thunder.
In episode 194 of Sailor Moon, rain begins to fall when Usagi collapses in tears because she can no longer bear the strain of wondering why her Love Interest in America hasn't written back to her at all. (Unbeknownst to her, he's dead.
In Monster, Tenma sinks to his knees to curse and bemoan the cruel fate that made him the savior of a murderer in the middle of a rainstorm. It's very sad, but the water getting on his pants is like the clothing equivalent of They Wasted a Perfectly Good Sandwich.
In Robotech, one of the episodes is called (A) Rainy Night, and is just that, a rather restrained, remarkably mature (in the proper sense of the word) conversation takes place between two of the major female characters about their love lives past and present, while a soaking rain comes down outside. One of the women is involved in a very dysfunctional relationship with a mecha officer, and the other tells her the story of how she met and got together with a by-then-deceased pilot. No explosions, no gunfire, not much comic relief, the entire episode is conversation and memories of a deceased character.
Code Geass: The entire colour palette is overlaid with grey after Shirley meets Lelouch having missed her date with him because she had to identify her father's body. Whose death Lelouch was responsible for. And things just get worse from there.
In Marginal Prince, Joshua sings four times in the course of the series. Twice the songs are about his feelings and despair and of course it rains in torrents during these montages.
It's raining in the Tokyo of You're Under Arrest! when Ken Nakajima becomes the victim of the "rogue officers" that cause accidents deliberately, and breaks his leg. He's seen laying down on the rain-wet pavement and grabbing his injured leg, much to the horror of his friends.
It also rains during several early episodes of Oniisama e..., while are also those were Nanako is most bullied and harassed due to being accepted into the the Sorority. Also, it's under a heavy and cold rain that Rei waits for five hours for Fukiko, not knowing that it's one of Fukiko's cruel mind-games. It causes her to fall extremely sick.
In Sakamichi No Apollon when Kaoru finds out his father has only come to gather his stuff and won't have time for a proper visit. Kaoru thinks about the things he wants to his father about but won't get the time to, like him making new friends and wanting to know more about his Missing Mom.
Kubo generally uses rain to show when a character or group of characters (sometimes even all of Soul Society) have fallen into despair. The overriding symbolism of this belongs to Ichigo, where even his Empathic Weapon hates the rain because of the despair it represents inside Ichigo's soul.
The surprising second to Ichigo turns out to be Ryuuken, whose dreams of saving the quincies were utterly shattered when he was a teenager. This is revealed in an arc titled "Everything But The Rain" that is primarily about how Isshin and Masaki met but which ends up revealing that the two characters associated with the rain were actually the experimental creation that was the ultimate source for Ichigo's rain-linked hollow-powers and Ryuuken, for whom the arc becomes one long devastating Heroic BSOD that changes his life forever.
Justified in The Sandman where the Dreaming reflects Dream's emotions. After Thessaly dumps him we see him simply standing and moping in continuous rain. Mervyn complains about this causing people to have dreams of existential angst and everyone in the Dreaming to get wet, while Lucien remarks that after Nada, the entire Dreaming was razed and stayed a wasteland for hundreds of years. In an interesting twist, the landscape does not change after he is forced to kill Orpheus although he is obviously upset and grieving.
Blade Runner. Only at the end is there clear skies, and even then, it's still drizzling.
This happens at the end of the 2010 film The Illusionistwhen Alice is told that magic isn't real.
A frequent motif of Akira Kurosawa. When his protagonists are at their lowest point, you can be sure rain will follow. Totally reversed in Ikiru ;the protagonist is so happy to have achieved his final goal that not even heavy rain nor snow can stop him from rejoicing in a swing.
Parodied in Hot Shots! Part Deux with the flashback to when Ramata leaves Topper. She sends him a card to break up with him. When it sinks in, it starts to rain but entirely localised to where Topper is standing.
In The King's Speech, after an argument, Lionel tried to see Albert to apologize. At the time, Albert's brother was planning to abdicate his sovereignty to Albert, so he was told that the Duke was "too busy" and shown to the door, where it was pouring rain outside.
Used literally in Men In Black 2, as the Light of Zartha leaves Earth.
It was either parodied or used very cheesily in Alpha and Omega. When it looks like Kate has been trampled to death by cariboo, everyone is very sad and the sky turns gray and there's thunder, then Kate wakes up, and instantly the sky turns blue again without a cloud in the sky.
This shows up in Tempest A Novel, when Jackson gets stuck in the past, it starts to rain. Justified in that time travel apparently causes rainy weather.
Live Action TV
The Killing is a show based on this trope. Every scene so far in the series has either been overcast, raining, or night. Granted, its set in Washington, but still...
In Sherlock, the titular character jumps from the roof of St. Bart's hospital, apparently commiting suicide, and as his best friend John tries to get to him the sky goes from partly cloudy to dark and rainy in a matter of minutes.
From the same episode: as John is describing the event to his therapist, and later when he's sitting alone in 221B, probably soon after the funeral, it's again raining heavily.
This is a common trope in country music to show that the singer is depressed or there is turmoil:
David Nail's "Let it Rain" involves the singer cheating on his wife and being thrown out into the rain (apparently inspired by the last scene of the movie "The Last Kiss").
Gary Allan's "Songs About Rain" is told from the point of view of an ex-boyfriend on his love's wedding day to someone else—and as he's driving around being depressed, all the radio will play are "songs about rain."
The Eli Young Band's "When it Rains", about a bad break-up.
Garth Brooks "The Thunder Rolls", about a wife discovering her husband's affair (or, according to the video, Domestic Abuse)
Blackhawk's "I Can Sure Smell the Rain", about an impending break-up.
Steve Holy's "Come on Rain", in which a distraught boyfriend begs the rain to delay flights at the airport so he can stop his girlfriend from leaving.
Rascall Flatt's "What Hurts the Most"; the singer mentions that the rain on the roof "don't bother me" but it fits with the mood of the song.
Carole King's song "Crying in the Rain" (also covered by A-ha) is about a person who's still not over a bad break-up and hopes it'll rain soon so they can cry underneath it and not let others know about their heartbreak.
Certainly at least invoked by "Cold Kentucky Rain".
"It Never Rains" (in California) ... it pours.
The art for the country of Eisen in 7th Sea player's handbook has this. Justified, because Eisen is based on post-Thirty Years' War Germany, which was a grim and depressing place.
In Katawa Shoujo, it rains during Rin Tezuka's second Bad Ending, when she tells Hisao "But Now I Must Go" and breaks up with him to take an art scholarship in Tokyo.
Happens twice in Saints Row 2: when the Boss has to Mercy KillCarlos after he is abducted and tortured and again at Aisha's funeral.
Urban Fantasy web series Broken Saints uses this in Chapter 14, Act 2, as one of our heroes, Kamimura, walks alone through a very depressing and disturbing section of downtown Coast City—reflecting his own display of sorrow at what he sees around him.
In Everyday Heroes, when Jane is released from prison, she walks away from her family (and her old life as a villain) through a cold February rain, alone.
The scene where the dwarves surround Snow White's bed and cry. She didn't die, per se, but still...
"Of course, everyone forgotaboutMe. Nobody remembers the rain cloud over me when everybody forgot my birthday. Figures."
It rains as Littlefoot of The Land Before Time finds his mother after her fight with the Sharptooth. It starts to rain harder as she dies.
In Winx Club S4 episode 24 it starts raining after The Wizards of the Black Circle escape after having used the gift of life on a dead flower, taking away the Winx's only chance to save Nabu who had sacrificed himself to save the Earth fairies.