In Ah! My Goddess, it turns out that plain old cola has the same effect on Belldandy that alcohol should ("should" being the operative word - She's a Norse goddess, and thus Never Gets Drunk). Fortunately, she's just as nice drunk as she is when sober, if not more so, which actually causes problems of a different sort.
Lucia in Mermaid Melody Pichi Pichi Pitch gets drunk off cola too in one chapter of the manga and spends the rest of the time worrying about what she can't remember. In the anime, this was further Bowdlerised into a magic emotion-controlling jewel.
In Keroro Gunsou, high levels of humidity can cause Keronians to act drunk, though this usually only affects Keroro. It also increases their strength, intelligence and reaction time. This is used to justify why the usually lazy and weak Keroro is the leader of his group: the humidity is just naturally higher on their homeworld, where he performs at peak efficiency.
Ryuk: I do handstands and my body twists up like a pretzel! It's not a pretty sight!
It's unclear whether or not Ryuk was lying about this. He does get really weird when he doesn't have apples, but when he becomes unable to communicate with Light for a long time he snaps out of it immediately and goes about his business. It's possible that he just really likes apples and is trying to annoy Light into giving him more.
Lum and Ten from Urusei Yatsura would get drunk off of "umeboshi" - otherwise known as pickled plums. Note that they're otherwise immune to alcohol, drugs and poison. It's one of those "reversed reaction" things - in Japan, they're commonly eaten as a hangover cure.
There was also an alien fruit juice that had that effect on humans (and not on oni).
Of course Vriska loves that shade of blue. Of course Karkat canít seem to get away from it. The smell is intoxicating, but the undercurrents are too bitter to make it truly wonderful.
They smell so delicious together, the two of them, Vriska and Karkat. A wild, crazy blue offset by a shocking, angry contrast that swirl together in her minds eye, so decadent she could lick it forever and never get tired of the taste.
She smirks, and after a moment of silence the scent of bright cherries floods the air. Tereziís knees go weak at the smell, and she opens her mouth, trying to taste as much of it as possible. Blueberry throws itself into the mix with wild abandon, and itís the more wonderful than she could have ever imagined. Colors burst in her mindís eye, and she moans from the taste itself, senses overrun with pure pleasure.
Diaries Of A Madman has quite a few, but the naga are probably the most extreme example, as mercury is used as a recreational drug.
Films — Live-Action
The Newcomers in Alien Nation get drunk on sour milk. Alcohol has no effect on them.
In District 9, the alien Prawn have a voracious hankering for cat food. Black markets spring up for the stuff and all. We can speculate they get high on tyrosine or taurine in the fish protein — other food would do it, but cat food is good — and cheap. Or it is just using the Rule of Funny.
In Amanda And The Alien, the titular alien discovers that for him/her/it, paprika is a powerful aphrodisiac.
A deleted scene from Buckaroo Banzai establishes that the Red Lectroids get a narcotic effect from sucking on dry cell batteries.
Alan Dean Foster's Humanx Commonwealth is littered with strokes of genius, and Alien Catnip is regularly referenced as a consequence of Playing WithNo Biochemical Barriers - the majority of species can breathe the same atmospheres and eat the same food, they just don't find it comfortable. It's the little things that get them - for example, the racoon-like Tolian race is unaffected by alcohol, and instead gets smashed on the lymphatic fluids of certain animals. One that drives drug cops of all races into conniptions is that just about every race has something that some other race considers high-value drugs as part of their essential diet.
In Frank and Brian Herbert's novel Man of Two Worlds, ordinary basil acts as a powerful psychoactive for the Dreens, Sufficiently Advanced Aliens who created most of the universe with their thoughts. They call it Bazeel.
Instant maple and ginger oatmeal is addictive to Yeerks, makes them lose control over their hosts, replaces part of their brain stem, and drives them crazy. Yes, the characters realize that it's absurd. It veers into the horrific when you realize that the oatmeal also removes the Yeerk's need to leave its host head occasionally, and it makes the Yeerk immortal. The poor host is going to have an insane alien slug in his brain till he dies.
Jake: Battles involving oatmeal are just never going to end up being historic, you know?
Ax seems to develop a near addiction to anything related to taste, as his species normally have no sense of taste. Some of the things he enjoys gorging himself with include: cinnamon buns, chili, engine oil and cigarette butts. The human race ends up exchanging doughnuts for alien technology.
In the Young Wizards series, chocolate has a variety of effects on different alien species; it acts as a drug for some, but others just like how it tastes. It's also why UFOs really visit Earth. Carmela forces an entire battalion of aliens to back down by threatening a wrapped chocolate bar in the eighth book.
In the Star Wars Expanded Universe the Arcona can become addicted to table salt, and there's even a quick and easy indicator. The entry in the Essential Guide to Alien Species features an excerpt from the journals of Mammon Hoole (a member of a species of shapeshifters who uses his abilities to further his job as an anthropologist when the local species is likely to eat outsiders) describes an encounter he had with a young male of the species who was ready to mate, and had gone through a depressingly logical and tedious process to decide which of a selection of females it was going to be. When the young man, with Hoole in tow, reached the domicile of the lucky woman, he was shocked to find that since he had last seen her, her eyes had turned from green to gold, giving away her salt addiction and marking her as unsuitable for mating.
Another character, who had started training at Luke Skywalker's Jedi Academy, became salt addicted when Tionne Solusar made her famous pot roast for dinner. Two days later, all the salt in the Academy was gone, and the gold-eyed Arcona was kicked out.
In The Company Novels, chocolate (referred to as Theobromos) is the only thing that can intoxicate the time-traveling operatives, and thus you get things like one character having a "dealer" in premium chocolate.
In Sweet Silver Blues, Morley Dotes bribes a colony of brownies to spy on a mansion for him with sugar. They are later shown strewn all over the neighbor's lawn, giggling and stoned to the gills.
In The Belgariad, candy has a much stronger effect on dryads than on humans. One of the prologues even has Belgarath having to be very careful to avoid getting Ce'Nedra's ultimate great-grandmother hopelessly addicted to chocolate (he doesn't mind her being addicted to it, mind you — he just needs her able to function without it).
Twilight vampires will occasionally run into someone whose blood is like this for them, to the point of being nigh-irresistible. Like the main couple. To a notably lesser extent, any human's blood.
Butterbeer, in the Harry Potter novels, while mild to wizards, is depicted as being quite intoxicating to house-elves.
It's debatable just how "soft" butterbeer actually is. The simplest explanation is that it is a mildly alcoholic malt beverage: not enough alcohol to have a major effect on even a very young (Harry has his first nip at 14, and the stuff doesn't seem to be age-restricted like firewhisky) human, but if a house elf (roughly half the size of even an adolescent human) rips through a six-pack in under an hour, well.... We should note that historical Tudor-era Englandhad a drink called butterbeer, made of butter, eggs, sugar, nutmeg, and ale; it's not terribly alcoholic—since it involves diluting beer, and if you use a weaker English brew like session ale (beer in the 16th century would've been weaker, as it was the safe alternative to drinking water and the English hadn't gotten ahold of tea yet)—but still enough you could get drunk after a few pints. Here's one of numerous recipes.
In the Honor Harrington novels, the largely carnivorous treecats find celery irresistible. In fact, it was their pilfering of human celery that led to the first human-treecat encounter. Turns out it actually enhances treecat telepathy, as well as having the more expected effects of such substances.
In Mercedes Lackey's urban fantasy novels, caffeine is an instantly addictive drug for elves.
In The Witcher books at least greater vampires suck blood only to get drunk. There was even one abstainer — being cut into a dozen pieces buried separately for a century or so after overindulgence can drive the lesson home quite well.
Captain Future has two examples. First, one of the characters has a pet called Eek who eats metals, preferring heavy ones. Large doses of silver or gold were shown to make him rather drunk. Also, in one of the books, Otho (a shapeshifting android), disguised as a human, goes to investigate in a bar. First, he drinks a bottle of Gargle Blaster without any visible effect, then he orders wine... laced with radium chloride. That one works.
In the German SF novel Der Verbannte von Asyth, Earth coffee turns out to work (and apparently smell and taste) remarkably like the alien drug "klukol", basically an alcohol equivalent, on the eponymous protagonist's species.
In the Star Carrier series the Agletsch get drunk off of acetic acid (vinegar).
In Space Beasts, various Earth foodstuffs are dangerous to Extra Terrestrials and Magical Creatures, first of all Intelligent Herons The Aves have extreme reactions whenever they eat strawberries, they don't get addicted, but for the male Aves they seem to get a similar effect to when you mix ecstasy with Viagra. The Male Aves get a painful long-lasting erection and also they get a fierce desire to hump anything they can get their hands on. Zander ends up assaulting his own wife in public after tasting a strawberry, and Revel rapes the Ant Girl Yin after she force-fed him some strawberry champagne; both felt extreme shame and embarrassment once they snapped out of it.
As for Magical Races (Or more specifically their half human descendants) each species of Fae has its own drug: for Elves it's wasabi, for Fairies, peanut butter, for goblins, bananas, to half human/half Fae these addictions are extremely powerful, the only way to bring them 'back down to Earth' when they give into their addiction is through physical pain, normally that means a spanking.
Some species of Humanimal (Specifically Prehistoric Species like Dinosaurs) can be extremely sensitive to modern foods. Rodan the Pteranodon Man finds that Chocolate has the an effect on him similar to the effect that strawberries have on male Aves. He almost gets demoted when he rapes an enemy girl soldier.
Alien Nation has sour milk as akin to alcohol. Considering that milk contains lactose and does ferment if handled properly, this simply means that they really like kumiss or kefir, or just plain old yoghurt and cheese.
Since human cells and the bacteria involved in milk spoilage produce lactic acid under anaerobic conditions this might suggest that the aliens are more like fungi than mammals and produce alcohol when exhausted.
In Buffy the Vampire Slayer, Slayer blood is this for Vampires. It's also mentioned that a vamp can become high by feeding off someone who is high.
Spike: If every vampire who said he was at the Crucifixion was actually there it would've been like Woodstock. I was actually at Woodstock... that was a weird gig. I fed off a flower person and I spent six hours watching my hand move.
Apparently mold thatís poisonous to us humans is ďmeth plus heliumĒ to Wesen in the series Grimm.
On an episode of Sabrina the Teenage Witch, Sabrina becomes addicted to pancakes (part of an old Spellman family curse, of which there were many), and at one point gorges herself to the point of bloating. When she tries to go cold turkey, she experiences withdrawal symptoms, hallucinating that Salem is a pile of pancakes asking whether she is hungry, imagining that the school is putting on an elaborate musical number imploring her to eat pancakes, and dreaming that a giant syrup bottle tries to persuade her to come away to a haven for witches addicted to pancakes, where she can eat to her heart's content. It was a really weird episode.
One episode of ALF has ALF becoming addicted to eating cotton, which has lots of weird side effects on him such as causing him to dance around wearing a bowler hat and holding a banana while singing showtunes.
The page quote comes from this scene of Farscape. Later that episode, Rygel actually steals candy from trick-or-treating kids.
In a later episode ("A Constellation of Doubt"), Rygel comments out that most species consider refined sucrose to be an addictive poison. So it's existence wasn't unknown to him, but he was unprepared for the abundance.
In Torchwood: Children of Earth, the 456 use human children as a euphoric drug, incorporating the child into their physiology and getting high off the child's hormones.
To the Pyrians in Andromeda ammonium phosphate (fertilizer) is a highly addictive and deadly drug. One planet based their economy on smuggling it to them, when Captain Hunt found out that was why the Pyrian fleet was blowing up their freighters he stopped trying to help them.
In True Blood, the blood of people with Faerie ancestry like Sookie is intoxicating to vampires.
The Gua in First Wave can easily get addicted to table salt, although their High Command frowns on such weakness and orders the addicts killed. This was discovered by accident when Foster was interrogating a wounded Gua and poured salt on the open wound. The result was a seriously stoned Gua. Given the Gua mastery of genetic engineering, it's strange they don't remove this weakness from their hybrid husks.
Plushies in the German game PlŁsch, Power & Plunder can get addicted to washing powder if they have to go into the washing machine too often (which is the case if they get dirty).
Rayman 3: Hoodlum Havoc features hallucinogenic plums and alcoholic plum juice. Murfy claims that Globox's drunk reaction to the juice comes from being allergic, but Andre does say that the juice is better when fermented.
Hivers in Sword of the Stars have taste and smell organs that are wired in a way that strongly fermented human foods, especially cheese, becomes like mild narcotics to them. It's mentioned in the supplementary novels that cheese is one of humanity's main exports to the hivers.
On the flip side, raw, unprocessed garlic is dangerous to hivers because of their over-sensitive olfactory organs. Hiver warriors eat cloves of it as a manhood ritual.
Bender, being a robot fueled by alcohol, malfunctions as if heavily inebriated whenever he doesn't drink enough. He even develops a patch of rust around his mouth, mirroring a human's 5 o'clock shadow.
There's also an episode in which Bender gets high by overloading on electricity, complete with an LSD-reminiscent hallucination when he first tries "jacking on".
Anchovies are either addictive to Decapodians like Zoidberg (which led to anchovies being eaten into extinction), or they just taste ridiculously delicious. Or both.
The entire plot of schlocky Christmas special Grandma Got Run Over by a Reindeer happens because of fruitcake, which reindeer will drop everything and trample old ladies to get at.
Actually the only reason that the reindeer went after the stuff was because Cousin Mel had spiked it with what turned out to be reindeer nip in a plan to ruin the family business by making their customers ill.