Asuka Quest: Asuka (or more accurately, the person who accidentally bodyjacks Asuka) has a drunk phase early on in the quest. Her in-universe excuse is all of canon!Asuka's mental issues catching up to her, but the actual reason was more to escape the fact that she got stuck in theDarker and EdgierHumongous Mecha series. She drops it after the fiasco of a battle against Matariel, but not before she got Shinji into Dark Souls and accidentally revealed that she knew Rei was a Nephilim.
The Black Prince: Harry's excessive alcohol consumption is commented on repeatedly. Eggsy eventually calls him out on being a drunk after they break up.
Contraptionology!: Applejack's love of drink and brewing is played up to counterpoint her teetotaler Love Interest Bell Pepper.
Tenkei is commonly drinking beer, and got dead drunk during the party to celebrate summoning Mordred and Iskandar. According to Mordred, he drinks so much beer that it made his blood taste bad.
Iskandar picked up Tenkei's drinking habit. Even Tenkei complains about this, since his Servant makes the beer empty twice as fast as before.
War of Remnant: A RWBY Anthology has both Willow and Winter Schnee devolve into alcoholism as a result of their trauma. Willow after learning Jacques never loved her and their children, and Winter after the loss of her wife and daughter.
The Immortal Game has Sir Unimpressive, who's never seen without a flask of whiskey. Twilight at one point wonders where he keeps managing to get it refilled.
Frederick von Hohenzollern, the main hero in A Dynasty of Dynamic Alcoholism, is a devoted high-functional alcoholic - to the point he's never seen without a flask. Of course, the name kind of gives it away...
Earth and Sky: Prince Blueblood is sloshed in every scene he's in. Justified by the fact that being stuck in a loveless marriage of convenience with Diamond Tiara is hardly a state of marital bliss.
In Under the Northern Lights King Ukko is a bitter drunkard. Heavy drinking is socially mandated among reindeer, but he does it enough that even they react negatively.
Fallout: Equestria: Littlepip's mother always has a bottle nearby. She's a very high-functioning drunk, but she still mostly ignores her daughter. Her drinking habits also mean that Littlepip is one of the very few ponies in the small world of the Stable who doesn't know who her father is. When Littlepip finally returns to the Stable, after fending off the Steel Rangers who were assaulting the place, she notes that her mother is even more drunk than usual to deal with the trauma. The only obvious outward sign is that she's gossiping with her friends about how she had to suffer her dress getting dirty when a friend died.
Fallout: Equestria - Project Horizons: Blackjack never, ever passes up an opportunity to get wasted, especially when Wild Pegasus whiskey is available. Though seeing how she's been through more mental, physical, and spiritual trauma than nearly every fictional character except for Guts from Berserk, can you blame her?
In Boys do Tankary?, Vincent and Gage were this, apparently since the age of seven. They had fought in a war on opposite sides, and Nyra, who was Vincent's sister, but on Gage's side, got captured by Vincent's side, who raped and murdered her squadmates after taking her prisoner. When Vincent spared Nyra, they were put into a cell with a gun and told one had to kill the other by the end of the month, and Vincent complied; both he and Gage were driven to drink by the experience. Nyra, however, turns out to be alive, and Gage resolves to quit drinking.
We have Rei the drunk secretary from Kill la Kill AU and this has gotten her into trouble, as she's sent four kids on a beer run. Apparently, she is rarely sober, as she doesn't seem to be sober when she hired as a babysitter. Apparently, this is a deconstruction, seeing as we are shown the harmful consequences of her being one, i.e, she is mentioned to be passed out in her own vomit from time to time.
We have Ragyo, who is mentioned to be drinking red wine on a semi-regular basis until Chapter 14. She returns to that habit afterward.
Ryuko is too, to a lesser extent. Considering that the Kiryuins were revealed to have a large alcohol collection, it would safe to say that they all were or are.
Empath in the Empath: The Luckiest Smurf alternate timeline story "Papa Smurf & Mama Smurfette" turns into this after Smurfette marries Papa Smurf and has a child through him, and after he successfully leads a rebellion against the new couple that forces them and those that are loyal to them (which included Polaris Psyche and the Smurflings) out of the village, with Empath still being heartbroken from being spurned by Smurfette in favor of Papa Smurf.
Zeroninety's Jem fanfics The Mess I'm In and Lasting Fame portray an older Kimber as a recovering alcoholic who has frequent problems with relapsing. She has barely talked with her sister Jerrica in years as a result (not helped by Jerrica's own issues with her identity). A factor to Kimber's alcoholism was her divorce with Sean.
Arizona in Scary News out of Tokyo-3 gradually descends into addiction as impossible and disturbing events continue to pile up on him. He starts out in I Need a Freaking Drink territory, but his offhand references to what he's currently drinking grow more and more frequent; after a nervous breakdown that forces him into retirement, he does practically nothing but drink, and the quality and coherence of his posts vary wildly depending on whether or not he's sober at the time.
In The Undesirables, Lightning Dust has basically living in the bottle since she dropped out of the Wonderbolts Academy. However, after being recruited by Luna for her team, she's inspired to pull herself together, becoming more of a Functional Addict.
The My Little Pony: Friendship Is Magic fanfic Drop of Moonshine is comedic, however the backstory behind it is not. After banishing her sister to the moon Celestia began drinking the pain away to the point where she could barely function as princess. This led to ponies stopping the production of alcohol so that the princess would be forced to go cold turkey. Eventually Celestia straight up banned alcohol (and thus modern ponies don't know what alcohol or being drunk is). Celestia has been sober for over 900 years, though when Luna starts making moonshine she picks up on drinking again (albeit for fun). This leads to alcohol being legalized again in Equestria and reintroduced into society.
Forum of Thrones: After the reality of his poor life slowly hit him, Robb became this, especially after getting rejected by Harpy, the only woman he ever developed genuine feelings for.
Wind Breaker drinks a lot (but only enough to get buzzed, no more), and Night Blade, noticing this, fires him from a job for it during the former's Establishing Character Moment due to the laws against public intoxication. There's a legitimate reason for his drinking habit though - when he was a child, he couldn't stop from telling the truth and got into fights because of it, so his caretakers decided to give him alcohol to try and restrain his truth-telling. This happened when he was nine, and he hasn't been able to stop drinking since, though after earning his Element, he promises Applejack that he'll try and sober up and finally admits to himself and the others that he has a problem.
An unnamed Earth Pony was this in Wind Breaker's background. It's explained that he drank enough that one day, he forgot he wasn't a pegasus and tried to fly, only to fall almost eighty feet straight down, shattering all four legs on impact and only surviving because of a combination of his natural durability and one of the unicorns below managing to cast a cushioning spell on the ground at the last minute - if not for both of these factors, he would have died on impact. Instead, he's alive and has been completely wheel bound ever since, the experience resulting in him sobering up for good.
In Laying Waste To Halloween, Gabe, like his canonical appearance in Percy Jackson and the Olympians is an alcoholic. In this fic, Percy thinks he's better when he's unconscious from drinking so much or out drinking with his friends. He's worse when the beer runs out.
In My Huntsman Academia, Glynda Goodwitch is depicted as this to deal with her wacky, headache-inducing students and co-workers, downing an entire bottle of pricey Mistral Brandy every month to relax. She apparently once drank Qrow under the table.
As per his MCU self, Tony Stark in Child of the Storm drinks a lot during the first book, even keeping a supply of alcohol in every lab. If he's not on caffeine, he's probably on alcohol. However, he does cut down on it somewhat once his daughter Ada is born and he has a role model to set.
Coco is a Hard-Drinking Party Girl bordering on an alcoholic. She drinks both for fun and to deal with her experiences as a huntress-in-training. Her teammates think she drinks too much, but Coco insists that she's fine. Eventually she sees a therapist and is diagnosed with PTSD.
Qrow's drinking is Played for Drama compared to in canon. He drinks because of all the trauma he's had in life. Being forced to kill his lover Summer is his primary reason to drink.
Weiss and Winter's mother is a neglectful Alcoholic Parent. Winter's disdain for alcoholics is a large part of why she gets along so poorly with Qrow.
In Do You Believe in Fairies?, Owen's heavy drinking stems from his fear of being alone and his insecure nature, especially surrounding his sexual orientation. He's closeted because he dislikes being seen as "different" and doesn't like making things difficult for those around him.
A Prize for Three Empires: Carol Danvers develops an addiction to alcohol when she starts losing her powers. It takes a while until she owns up her alcoholism and starts fighting it.
Lapis is an alcoholic. The story starts with her calling her exe Jasper for the first time in two years. She needs a ride home because the bartender took her keys.
Jasper is recovering from alcoholism brought on by Lapis' abuse.
Lasting Fame: Kimber has been struggling with alcoholism for years. She was doing okay for a few months but relapsed when her daughter mentioned that her step-mother was pregnant.
A Diplomatic Visit: Discussed in chapter 9 of the sequel Diplomat at Large. When Fancy Pants comes to meet Blueblood with a bottle of wine, the latter implies that if he keeps this up, ponies who love to gossip might start thinking of him as having a drinking problem. Fancy rather firmly denies that he's an addict; his only drinking problem is when he has a good bottle and nopony to share it with.
King Thranduil of The Hobbit is very frequently portrayed this way in fanfics both serious and cracky, owing to his reputation in the fandom as the "dwarf-racist party dad".
June is seen drinking in almost any given episode.
Apparently, Alcoholics Anonymous banned June for life when she attacked the leader of the group for telling the group members to try to go a week without drinking.
Doug Funnie, probably to cope with being traumatized by Barney on three separate occasions (and because the Disney version of his show gave him PTSD).
Two words: Elmo Reddmonster. In fact, he founded Elmo's Tavern solely because there weren't any bars in Unnamed Town and wanted a place to drink at.
Another Day in Bluffington Duology: Doug Funnie became a drunkard in order to cope with everything around him changing. Even his morning routine starts with a glass of gin and water.
to want to drown his sorrows.