In Project Tatterdemalion, a quirk of genetically engineered biology means that people with Psychic Powers- shinigami and Quincies- really do need caffeine as a basic nutrient, especially when they use their powers a lot. Shinigami in particular also like it because it makes their hearts beat faster- the process that makes them shinigami slows their heartbeats way down, and caffeine brings it back to normal.
In The Magic of Torchwood, Owen runs on coffee. He is annoyed when he is without it. He spreads this irritation around. It is generally considered best to give him coffee to avert this.
Child of the Storm has most of the Avengers fitting this trope, with one of Loki's more marketable skills being an excellent coffee maker. Another notable example is Carol, who is reallyNot a Morning Person and requires caffeine to function. She's also capable of downing a steaming hot mug of coffee in one.
In the remake of Battle Fantasia Project, interfering with exports of Turk, Finnish and Italian coffee to Equestria is considered attempted murder of Twilight Sparkle, implying she is this. On the other hand, Pinkie Pie is banned from having any coffee whenever she visits Earth.
In the cracky fanfic Reload, a "Groundhog Day" Loop type fic that long ago reached the lets-goof-off stage, we have Sasuke (who is currently female, long story) get up and reach for the nearest cup of coffee. Naruto comments that it was boiling moments ago.
In the Sword and Shield Verse, a crime-based Pokémon fanfic, we have BrendaJohnson, our main OC character who's partnered with Mewtwo aka VahanSmith. Just Brenda, who prefers her coffee "liquid, preferably alive". On the other hand, Mewtwo has stoutly refused to resort to coffee. Brenda considers that a sign of insanity.
Toy Hammer: Commissar Tomas Sturm takes a liking to Terran "recaff" (a.k.a. coffee).
Commissar Steve's entire motivation in A Day in the Life of a Commissar is getting a cup of coffee. Justified, since his room-mate has night terrors and the beds are uncomfortable, so he barely gets any sleep. He goes completely berserk when he finds out Nathan Johnson, the Force Commander of the local chapter of the Blood Ravens, bought all the coffee on the planet. This escalates from teaming up with his Sitcom Arch-Nemesis, to challenging Johnson and his two friends ( The Librarian and Chaplain) to a cage match, to demanding the use of a Baneblade Super-Heavy Tank.
The Killer Dame is a parody of the episode "The Killing Game", in which Voyager's crew was brainwashed by the Hirogen into thinking they're characters in a World War II holodeck program. Reality Ensues when Captain Janeway finds to her horror that the only coffee available to civilians in German-occupied France is ersatz coffee made of crushed acorns! When American troops arrive, she's willing to violate her Celibate Hero status to get her hands on some real beans (fortunately the Doctor deactivates the brainwashing at that point).