At the start of the Twisted Tales of Felix the Cat episode "Nightmare on Oak Street", Roscoe is trying to drink as much coffee as possible so he won't fall asleep and be at the mercy of the episodes villain, a dream-weaving monster named Jeepers Creepers. It doesn't work though—he ends up falling asleep anyway.
In Men in BlackThe Animated Series, the "worm guys" entire function at MIB seems to involve making coffee (and getting into wacky shenanigans at the worst of times). It is revealed that on their home planet, only royalty can drink coffee, leading to their quick addiction to it once they reached Earth (Forbidden Fruit and all that). One episode has them saving their king's life and requesting the right to freely drink coffee as their reward.
One episode of Dexter's Laboratory shows how Mom and Dad are in the morning before they have their coffee (yikes!), but once they have it they magically transform into their "normal" selves.
And the plot of the episode is, of course, that the kids have stolen their coffee overnight, Dexter being curious how coffee changes them.
Tweek from South Park is absolutely addicted to coffee, and as a result is very twitchy. His parents (who give him the coffee) think his twitchiness is due to ADD.
Things are different now that we now know that Tweak's not addicted because young kids shouldn't drink coffee - he's addicted because the secret ingredient is Meth. His dad slips it in his coffee and Tweak has no idea.
Wyatt from 6Teen always has coffee every day. One time he couldn't get coffee, which let him have very little energy.
Futurama episode "Three Hundred Big Boys" involved Fry's attempt to use his 300 Tricky Dick Funbucks (read: "tax refund") on 100 cups of coffee. Despite getting unbelievably jittery, irascible, and otherwise fucking wired, he arrives at this goal. Somehow. Apparently, when you hit #100, you attain Caffeine Bullet Time.
In Beast With a Billion Backs, the crew is shown to have a pre-mission ritual of receiving scalding-hot coffee enemas.
"Mountain of Madness" starts with Mr. Burns arriving at work all chipper and energetic; when Smithers offers him his coffee, he turns it down, saying he doesn't need it. Then, over the span of about five minutes, he slowly nods off, and starts to fall asleep, until he weakly says, "Smithers... cof... fee..." (He snaps back awake when he gets it.)
In Jackie Chan Adventures, Uncle orders either Jackie or Torhu to "Get in kitchen and make coffee! Uncle need caffeine!"
He gets very irritable if he doesn't get it. "You forgot to make coffee this morning! Coffee is the only thing keeping Uncle's ancient heart beating! You want dead Uncle?! NO?! THEN YOU MAKE COFFEE!!"
This is a major plot point in the episode Caffeinated Concert Tickets of Regular Show.
In The Powerpuff Girls episode "Power Lunch", Lil' Arturo drinks a cup of coffee followed by the whole pot.
The revival episode '"Super Sweet 6" has the Professor going on a frantic coffee binge at Princess Morbucks' birthday party.
In Space Ghost Coast to Coast, Brak famously states "I don't like coffee. It makes me jittery. Here's an impression of me on coffee: DS;5w23LFKJP70IEU@Q)O($*#@05rsldkfjxxx. Hey, whaddayadoinwhaddayadoinwhaddayadoinwhaddayadoin? I don't know what I'm doin', cause I've had too much coffee! AAAAA! Don't drink too much coffee, kids."
In the Cartoon Planet episode 'Tom Foolery', Zorak explains that his bad temperment is from giving up coffee;
Danger Mouse: The episode "Ee-Tea!" has society as a global whole ground to a halt after Baron Greenback steals all the tea there is.
Bobo (especially after a rough night) in Generator Rex. In "Crash and Burn", he finds the coffee maker is empty, so he eats the coffee grounds.
A Compressed Vice version of this is shown in the season 3 finale of Bob's Burgers: when Bob gets an espresso machine, Tina tries the first cup, and she gets instantly addicted to coffee. While the effects of the caffeine are the usual, her symptoms of withdrawal seem more akin to much harder drugs.
Used as a one-scene gag on Kaeloo, where the eponymous character gets addicted to coffee, which is never brought up again.
We Bare Bears: In "Coffee Cave", the bears start a coffee house in their cave and Ice Bear becomes addicted to the point where he starts eating coffee beans whole and eventually tries to kill his own brothers to get more.