7 Seeds: Ango takes one during the Hail Of Corn arc when he realizes the truth about what the term "Dropping Out" means and that the friendship bracelet he found actually is red, meaning it's Nobara's.
Ai no Kusabi: In the OVA after Riki's gang is attacked Riki takes one, reminiscing about all that has happened.
Henry from Digimon Tamers after Terriermon digivolves, where he reflects on his duties as a Tamer and his pacifist beliefs
Higurashi: When They Cry has a few of these too. Keiichi finds a depressed Satoko passed out in the bathtub from being in the hot water for too long.
It's more complicated than that: She was hallucinating that her abusive uncle had told her to stand under the boiling hot water and count to 10,000, since moving into his house meant she stopped getting treatment for her Hinamizawa Syndrome. She went along with all of the horrible things he did to her because of a combination of guilt (blaming herself for Satoshi's disappearance), blackmail (he constantly threatened to burn down Satoshi's room), and plain old fear. Yeah, Satoko has it rough.
Kaede Fuyou in SHUFFLE! goes Yandere on her friend Asa when the boy they both love, Rin, shows interest in her. She has one of these before climbing into Rin's bed naked to cuddle with him.
Perfect Blue: After Mima endures a good deal of disturbing hardships, she partakes in a hot bath which she screams into as she hugs herself underwater.
Yu-Gi-Oh! GX: During the aftermath of his traumatic loss to Edo and being demoted in the pro leagues, Kaiser Ryo Marufuji takes a shower after losing yet another duel, while reminiscing about being fired by his sponsor. He's freaked out by the end of the episode.
Averted in the manga, when the cartoonist behind it, Kotaro Mori, gives you a complete view of her naked body, with boobies clearly visible. Yeah, Mori, a good time to see a woman naked is when she's just had her heart BROKEN.
In Classi 9, Bach is seen in the shower after finding out about Rentarou's biological sex, trying to deal with that revelation.
Berserk: After being raped by a newly-demonic Griffith, Casca is seen sitting fully-clothed under a waterfall.
Also Griffith, after he becomes a prostitute to make money, complete with a wonderfully disturbing scene of him angsting while clawing at his arms until they bleed when washing himself. He only stops when Casca tearfully embraces him from behind.
Done by Asagami Fujino in Kara no Kyoukai; in her case, she actually was raped. The value of this scene jumps to eleven when the film adaptation came out. Then again, she becomes a psychotic murderer who is simultaneously terrified of her powers and unconsciously leering at the horrid violence.
Chrome Shelled Regios: Nina tends to do this when upstaged by Layfon, or losing a battle to another platoon.
Utena has one in episode 37, after finding out about Anthy and Akio.
Mr. Magnificent Bastard Lelouch Lamperouge from Code Geass did this once, after Shirley's father's death really made him confront the consequences of his actions. It actually managed to humanize him after all the killing he did. (Of course, by the end of the shower he decided that the best way to ease his troubled conscience was more killing.)
You can also count Milly in as well, when she was in a depressed state for a while after Nina told her off in R2 (while everyone else during bath time were happy and giddy with their upcoming date with Lelouch). This happened near the beginning of episode 12.
Happens twice in Re: Cutie Honey (once after a shouting match with Natsuko and once after losing it in a battle aganst Black Claw). The first one turns into a Shower of Awkward when Seiji decides to tag along with Natsuko in pulling her out of her rut.
Nodoka of Saki had one of these in the second episode of the anime after her loss and subsequent argument with Saki.
Saki herself on one occasion. She and Nodoka go over after they notice that some of Nodoka's old friends have reached the semi-finals, but Saki stops short after realizing her sister is in there and having a flashback. Saki can't bring herself to go in, goes back to where they're staying, and has a shower like this.
Faye Valentine of Cowboy Bebop has a Shower Of Angst scene after she recovers her lost memories.
Tsuzuki in Descendants of Darkness has a private Shower of Angst after being possessed by the demon Sargantanas in the Devil's Trill Arc.
Double points for the shower drowning out his vocalizations of misery while losing to the Enemy Within.
In the Captain Tsubasa Road to 2002 TV series, Koujirou Hyuga is seen showering and then punching the stall's wall in rage after clashing with Willem violently in his first training session in Italy.
Fushigi Yuugi doesn't actually feature Miaka in a shower (she's in a lake), but it still has that same effect as she furiously scrubs herself with twigs to the point of bleeding in the hopes that it would purify her after Nakago had raped her. Of course, he didn't really get to do that.
Also in the EikodenOVA, Mayo starts fading away, just about when she starts to feel guilty about how she'd been acting. The fading makes it worse, as she believes she's disappearing forever. She stands under the waterfall at the palace (which she had spurned previously on the grounds that it was an open-air bath), crying and upset. Mumin comes to talk to her, and is visibly concerned when Mayo fades again.
Gundam SEED was fond of these, providing shower scenes for Kira, Athrun and Cagalli (if memory serves). Oddly enough, the TV episodes had Cagalli moping in a bathtub, while the movie compilations changed it into a shower scene for no apparent reason other than to show a little more skin.
Tieria Erde is seen having one of these in Gundam 00.
Erza has one in the 23rd episode of Fairy Tail after retreating in a battle against Phantom Lord.
Lucy has one after losing her fight against Flare Corona.
In RahXephon, Elvy has one after one of her fellow pilots is killed. Ayato also evokes this trope by stumbling into a bathroom during one very angsty scene and getting wet by breaking the shower faucet.
Simoun likes this trope a lot. Paraietta had an attack of guilt or two in the shower while reflecting on her Attempted Rape of Neveril.
Ichise from Texhnolyze takes one in the first episode.
Occurs several times in the yaoi manga Under Grand Hotel mostly because whenever someone's taking a shower there's a chance they'll either end up getting raped or beaten up and then left there for a bit under the running shower.
Gankutsuou: Albert takes one in episode 8. (Sitting in the tub while the shower is running with his head bowed.)
He takes another one in episode 14, musing over the threat "disaster will befall your house as well!" Peppo even states "you've been in there for a while."
Legend of the Blue Wolves has a particularly chilling example. Jonathan is shoved fully clothed under a running shower for a moment before being approached by a nude Captain Continental who intends to rape him.
A variation exists in Naruto. Orochimaru is desperately waiting for Sasuke to arrive and provide a new body but his arms have finally reached their breaking point. As he stands in a shower, they begin to flake off and crumble. Despite his agony, Orochimaru is driven to rage when he must finally accept he needs a new body now and can't wait for Sasuke.
D.Gray-Man: Lenalee takes one on the ship to Japan, highly upset by Allen's "death".
In Future GPX Cyber Formula, Miki Jounouchi has one in an episode of Double-One when she thinks that Clair is a better worker in the Sugo team than her. In fact, this is a recurring theme in the OVA series, as evidenced by Asuka Sugo in SAGA and Kyoko Aoi in SIN.
In Noir, Mireille takes a shower when she decides to kill her uncle, who raised her after her parents were killed in order to protect Kirika.
Tira takes one in one of the Sorcerer Hunters side novels after a big fight with Carrot.
Rei also has her moments of these more than once. Considering that she is a Broken Bird, it's pretty understandable.
Fukiko is seen having one after Rei's death.
In Teacher's Pet Misuzu takes a Shower of Angst after she's raped by Masahiro.
In Axis Powers Hetalia, Lithuania is seen having a bath of angst in Poland's house, and we get to see the scars on his back.
In the Little Busters! anime, we briefly see Komari taking one during her BSOD. She has one in the visual novel as well, and while we don't see it, we do see the immediate aftermath - a just-dried girl with wet hair wearing a guy's shirt for pyjamas manages to achieve a similarimpact.