If a device requires a power cord to work, it presents a weakness, especially in the case of a Killer Robot, Powered Armor or other machine that needs to move around. But even stationary ones that have the cords running where people can trip on them can play this one for drama or laughs.
Alternately, the cord is just a few inches too short to reach the outlet, and there's no time to find an extension cord.
Very often intersects with Cut the Juice, when the plug is pulled, although the plot can also revolve around preventing that from happening.
The titular EVAs need an external power source to operate for more than a minute at full capacity or five minutes in a weakened state, and an early episode even has Shinji do a power cord transfer at one point to move into an area that his current cord doesn't reach. An attempt was made to copy the S2 engines the Angels used, with disastrous results—although it was implied to have been sabotaged. Unit 01 ends up just taking one directly FROM an Angel.
In the 3rd film Rebuild of Evangelion 3.0 Q, this problem had been overcame with portable batteries (granted they had a 14-year time frame to invent one).
In Digimon Tamers, the D-Reaper starts out as an amorphous blob of goo, but learns to make solid constructs by absorbing a video camera. Because it was plugged in, all of the D-Reaper's "Agents" are attached to the main mass by very long cords. Cutting the cords at first greatly weakens Agents, but eventually cutting a cord is all it takes to make any Agent instantly revert to gunk. However, the larger ones have multiple, gigantic cords and so it's easier said than done.
In the Marvel ComicsNew Universe title, Spitfire and the Troubleshooters, where the fugitives are attacked by a robot tank. While the hero fights it in her Mecha, the Troubleshooters frantically try to stop it themselves by trying to hack into its remote control frequency, only to be unable to find it. It turns out that the tank is controlled and powered through a really long physical power cord from the operator so hacking into its control function through radio waves is impossible. Fortunately once they know this trick method, that means Spitfire then just needs to find the cord to cut it and stop the tank.
In the film Help!, a Mad Scientist has a lab full of assorted devices, but keeps having to change the plugs to work with the power supply.
Back to the Future: Doc Brown needs to connect a power line from the top of the clock tower (where the lightning bolt will strike) to ground level, where the DeLorean will use the energy to travel through time. Unfortunately, the power cord isn't long enough to do the job, so he has to improvise.
Since the eponymous weapon in The Jackhammer Massacre is electric, this crops up. But not very often, since the cord seemed to be absurdly long.
The Adventures of Sharkboy and Lavagirl contains perhaps the most literal example; some of the cronies utilized by Mr. Electricidad are literally powercords. This seems too easy, right? Reach the maximum distance they can stretch and you can beat them easily. Have no fear, though: they can plug into other powercord mooks for a shocking train of baddies.
In The Naked Gun 2˝: The Smell of Fear, Drebin accidentally defuses a nuclear bomb by tripping over its power cord, after shouting 'Let's get out of here!' with only 2 seconds left on the countdown timer.
In one FoxTrot arc, Roger bought a giant mobile phone that needed to be plugged into the mains to work. Andy pointed out how that defeated the 'mobile' part of 'mobile phone'.
Get Fuzzy. In the strip for February 26th, 2013,. Bucky has come up with a wacky invention: a fan that's attached to a person's backside to keep their wallet from overheating their bottom. Rob Wilco wears it as a test, but complains that he can't move far due to the 3 foot power cord plugged into a wall socket.
Adventure Send in the Clones. One of the R&D devices the Troubleshooters must test is a belt device that generates a force field around the wearer. One of its limitations is that it has to be plugged in to work, which will severely limit the user's mobility.
Adventure "The Yellow Clearance Black Box Blues". The Troubleshooters are issued a Maxwell-Effect Moleculokinetic Field Device. It requires huge amounts of power to activate (too much for easily portable sources like power packs), so when the Troubleshooters go Outside of Alpha Complex they'll have to plug it into their vehicle's power supply. This will effectively prevent them from using it while away from the vehicle.
Supplement Acute Paranoia, adventure "Me and My Shadow Mark IV". When the Mark IV warbot was first designed, Power Services insisted that be powered by a long cord attached to their generators. Since the Mark IV was intended to operate in the Outside beyond Alpha Complex, this demand was ignored.
In Girl Genius, Anevka is a clank (robot) body created for a fatally injured noblewoman. She needs to stay connected to the large container where her actual body is kept in stasis. Near the climax of the story arc, the cables are cut and she freaks out when she feels no different — it turns out the real body is long dead inside the container and she has become an autonomous A.I. with Anevka's memories
The Megadoomer in Invader Zim, which was a robot death machine that had to be plugged in for power due to a dead battery.
On one episode of Teen Titans, Starfire travels to a Bad Future where the titans ended up splitting. Cyborg was the only one who stayed on the tower, because he had long ago burned all of his internal batteries, so he had to be constantly plugged to a large machine to keep functioning, and couldn't go anywhere. He comes back to help by toting around a large external battery and and repairs them at the end of the episode—Starfire returning to her time possibly preventing said future from happening in the first place.
One episode of Carl Squared has the protagonists being chased by a doctor wielding a power drill. He chases them across the street and the power cord reaches its limit and pulls the plug out of the outlet. The doctor laments about not spending a few extra bucks to purchase the cordless version of the drill.
On The Brave Little Toaster, the appliances need to find a way to leave their cabin to find their master, but need to stay close to an outlet to stay alive. The solution: a car battery attached to a rolling chair.
A strange mystical example happened in the animated version of Conan the Barbarian in which Conan fights a near-invincible foe only to learn he is powered by a wizard using what is essentially a magic, invisible power chord of mystical energy. Defeating the foe involved finding a way to sever the energy connection.
The page quote Season One of X-Men: The Animated Series. Master Mold, attempting to escape from the dam-based factory in Genoshia, takes a few steps from his chair, only to find out that he's plugged in by the back of his leg. The page quote is his last words before he's swept away by the raging waters.