Scott Adams is very fond of using playing with this trope in Dilbert, perhaps more so than in most series. He takes it to both logical ends by showing the workers suffering when the secretary replaces their regular supply with decaf, as well as his titler character gaining Psychic Powers when given an unlimited supply of coffee. Wally is the most extreme example. When Catbert and the boss order him to cut down to 40 cups a day, Wally screams "Not Double Digits!". The strip that best illustrates the Pointy-Haired Boss' evil? The one where he finishes the coffee without refilling the pot.
Played straight in Adam@Home.
Garfield strips, especially later ones, sometimes use coffee-addiction gags. A funny variation is when Jon was sitting calmly, while all of a sudden a clearly unhinged Garfield slams a mug on the table and screams "BEAN ME!" Jon simply notes that Garfield's probably had more than one cup of coffee that day.
And there's also a little flash "game" on the official site where you can feed Garfield coffee and watch him wake up and become more and more unhinged. It's aptly named Bean Me!
In one strip, Jon goes to pick up a cup of coffee; Garfield screams frantically for him not to drink it, but he's too late. Jon drinks it, and then falls asleep. "That coffee was decaffeinated, you fool!" shouts Garfield.
A Running Gag in the comic involves Roger, the head the Fox household, being rather non-functional, sometimes to the point of Cloudcuckoolander-ness, without his morning coffee.
One arc had Andy decide Roger was depending too much on coffee and cut him off cold turkey. After a hearty breakfast of raw macaroni in vinegar (thanks to Jason), he crashes down the basement stairs. When he arrives at work, he manages to attend several meetings, take part in a conference call, and give a lecture to younger employees on key company policies. Around two in the afternoon, he realizes he's in the wrong building.
Another comic has Peter weaning himself off of coffee, remarking that he drank so much during finals, if he went cold turkey, he'd die. When asked if he was drinking half-decaf, half-regular, he remarked "quintuple espresso".
Another of Peter's stay awake at all costs brews is coffetea (tea brewed with coffee), which is apparently just this side of a controlled substance.
In one arc, Paige uses coffee-tea in quantities that shock even her brother, which is quite a feat.
Speaking of Roger, on one occasion he was so out of it that he tried to pour his coffee into an upside-down mug. When Paige helpfully pointed out his mistake, he flipped both mug and coffeepot.
Paige herself is rather inept at the concepts involved in the culinary arts, even to such a degree that she uses a cup of grounds to a teaspoon of water. I'll give it one thing, it wakes her folks up.
"The pot's over by the fridge... The fridge is over there... See that thing with the blinking red light?... Roger, that's the answering machine." The last line said as we hear slurping sounds from off-panel.
In one strip, Peter comments that you know you've made coffee right when it's the fumes that wake you up.
In one strip, Roger takes a sip in the first panel, followed by a Beat Panel, then a look of absolute, complete shock. In the last panel, Jason is holding the coffee pot, and says, "You said to make it strong," followed by Roger - from the ceiling - saying, "Funny, I wouldn't have thought my fingers could grip like this..."
At one point, Roger goes in for a physical. When the doctor asks how much coffee he drinks in the morning and he replies "a coupla things of coffee." The doctor says "Two cups of coffee is OK. What else?" "Pots, not Cups."
One of Peter's bright ideas to stay up long enough to finish a book report was to mix an entire jar of coffee crystals with hot water and drink it all at once.
Subverted in one Bloom County strip, with vice-presidential candidate Opus stumbling around in a morning stupor, mumbling about needing coffee. Then he reads a newspaper. BOING! "Who needs coffee when you've got the latest poll results?"
Phoebe from Zits, who list "caffeine" as her religion when she applies for a job at Fourbucks Coffee. And has an espresso machine in her locker. In one strip, Jeremy taps her on the shoulder to ask her something and she hits the ceiling - literally - in shock, having drunk more than usual for finals.
One early The Far Side cartoon showed an angry man holding a smoking shotgun, having killed two people with it, while his wife behind him angrily says, "That settles it, Carl! From now on, you're only getting decaffeinated coffee!"
In Peanuts, Linus' "Blanket Hating Grandmother" likely qualifies, seeing as in one storyline, she drank 32 cups of coffee in one sitting! Unfortunately, Linus got the entire family angry at him for saying her dependence on caffeine was the same as how he depended on his blanket, leading him to seriously regret saying it and going to apologize to his grandmother. (And a small Crowning Moment of Heartwarming at the conclusion.)