In the Aqua Teen Hunger Force episode, "Dummy Love", the Aqua Teens make many attempts to get rid of or otherwise destroy the two Demonic Dummy characters that appear in the episode. Of course, no method of destruction prevents their return, eventually leading to a profitable and lucrative magic show career on the part of one of the main characters.
In the Batman Beyond episode "Sneak Peek", Terry does an extended chase scene following Ian Peek down floor after blockaded floor as fast as he can. The instant he falls through the final floor (right after Terry arrived), an elderly Bruce Wayne appears...although he was left hundreds if not thousands of feet away in no rush to chase after them.
It's actually parodied it also. In "Tortoise Beats Hare," Cecil Turtle and and Bugs Bunny are in a race, but Cecil gets his (identical) relatives scattered across the route ahead of time to screw with Bugs and make him think this trope is in effect.
In Animaniacs this is the main forte of the Warners, to the dismay of other characters.
A particularly funny one happens when they're antagonizing the Jerry Lewis-like Mr. Director. As part of his angrish fueled rant at witnessing this, he briefly points back to where they were, and for that brief second, they're still there.
The main page image from Histeria! comes from a scene in which Loud Kiddington pulls this on George Bush after he climbs over the gates in front of the White House. As you can see, the animators drew Loud twice on the same shot.
Parodied in The Simpsons a few times. In one, Mr. Burns makes it from the top floor of his mansion to his basement, faster than the kids can slide down a laundry chute, apparently only needing secret passages to do so.
In the safari in Africa, there's a P.O.V. Cam shot as Marge looks at a cheetah through binoculars. "They don't look so fast to me." Then she lowers the binoculars and the cheetah is right up in her face.
Nelson manages to do this trick in "Das Bus."
When Edna Krabappel first arrived in town, Moe pretended he wasn't a bartender so she'd date him. To keep up the ruse, he threw all his patrons out his bar and realized how often Barney was thrown. When asked how he managed to get back in so fast, Barney said that, as a drunkard, he doesn't know how he does the things he does.
Ron has this ability in Kim Possible. Kim leaps off a building with her pistol grappling hook, through a window, across laser beams to her target, Ron casually walks into shot seconds later and continues the conversation they had on the roof.
The Phantom Blot performs this in Mickey Foils the Phantom Blot, when Mickey uses tape on his shoes to get to the top of the Blot's blimp, the Blot's already at the top, after he fought Mickey on the ladder on the bottom of the blimp.
In the Columbo parody Mumbly (basically Wacky Races's Muttley in an overcoat and The Alleged Car that literally falls apart when parked) the Droopy example is revisited. The Columbo-esque villian keeps running away from Mumbly, only to have him turn up in places like garbage cans or under a serving plate lid a waitress served to the bad guy.
A lesser example appears in the Ben 10 episode "Ben 10,000". When Ben first meets his older self, he manages to cut him off at every escape attempt to continue the conversation. What makes this odd is that the older Ben is XLR8 at the time.
Used by Max Tennyson to escape Albedo in the Ben 10: Alien Force series finale. Ben uses it to elude Max in the very next scene.
She does this in the book as well, with the same justifications and implications.
In the animated adaptation of The Phantom Tollbooth, Officer Shrift moves from one side of Milo's car to the other... while Milo was looking right at him and talking to him. How (and why) he does this is never explained, but it's probably just Rule of Funny.
Amentia of Winx Club does this when chasing around Brandon in her bedroom, though since she's a nimble fighter she probably just moved really fast.
Parodied in SpongeBob SquarePants, where you can see the whole scene, but you still can't tell what happened.
Squidward: (picks up SpongeBob off his arms) "That's great, SpongeBob. Why don't you work on this problem back in the kitchen?" (throws him in the kitchen but SpongeBob reappears beside him.)'''
SpongeBob: "I'm serious, Squidward! Mr. Krabs is a robot, and I can prove it, too!"
Squidward: (looking around confused) "How did you...?"
A few times in Ed Eddn Eddy: In "Wish You Were Ed", Ed got stuck in a mailbox somehow, and Eddy and Edd ask Rolf for help. Rolf goes off on a rant about how much he misses The Old Country and doesn't help them, but then Ed appears right next to Eddy.
Ed: Rolf's homesick, Eddy.
Eddy: Where'd you come from?!
Ed: Blame my parents, Eddy.
Also in The Movie, Edd stops in his tracks completely stunned by something Eddy said. The camera follows Eddy and Edd up a hill...and then Edd is shown on the hill right there, stopping them.
Pinkie Pie of My Little Pony: Friendship Is Magic is surprisingly adept at this. In "Over A Barrel" for instance, she's shown in a train car along with the other main ponies prior to a commercial break. At the end of the break, the others reveal they somehow have lost track of Pinkie. Cut to Rainbow Dash by herself sneaking through the desert when Pinkie Pie shows up out of nowhere and startles her. Also, at the beginning of "Griffon the Brush-off", Pinkie keeps pulling this as Rainbow Dash tries to avoid her. Another example occurs in the season 2 premiere, where Pinkie hops outside to play in the cholocate rain, only to appear back in between her friends in the very next shot.
She's able to pop up in improbable spaces (like the inside of a piano without disrupting the song Spike's playing on it, the inside of a large bell that Rainbow Dash hid in to avoid her) or impossible spaces (a bucket of sponges much too small to fit a pony, appearing as a reflection in a mirror). Fanon has stated that because she knows she's a cartoon character, she's able to manipulate cartoon physics. She may also be completely insane (yes, just like Deadpool.)
The alternate Pinkie of the human world was even able to exit the screen by the left and appear to the right while Twilight Sparkle was facing left watching the exit, making it unclear just what Twilight saw. Of course, human Pinkie is even more impossible than pony Pinkie (pulling one of the balloon designs off of her dress and blowing it up into a real balloon comes to mind...)
For another Hasbro example, in Littlest Pet Shop (2012), Whittany and Brittany Biskit repeatedly give a Creepy Twins vibe by appearing in front of Blythe as she walks away from them.
Brainy in Hey Arnold! does this as a Running Gag, where Helga recites love poetry to Arnold only to be interrupted by Brainy, who she then punches. Most of the times, it's rather plausible as to how he gets behind Helga, but there are times where he literally shows up out of nowhere, such as on Elk Island and on a haunted train. It's also lampshaded at the end of "Helga on the Couch" where she ducks into an empty alley after making sure it's empty...and sure enough, Brainy comes to interrupt her.
In an episode of Invader Zim, GIR is sleeping on Zim's head but is forced off. The camera eases in while Zim delivers his Evil Gloating - as soon as the top of his head is Behind the Black, he yells at GIR for sleeping on his head again.
It's Robin's shtick in Young Justice. It starts to bug Kid Flash.
Even Batman gets in on the act, using it in the season 1 finale against Robin.
Mr. Buns from Ruby Gloom is a stuffed rabbit that can do a variety of things, including moving around, but only when he's offscreen.
Lampshaded in the Adventure Time season 5 premiere when Farmworld!Finn runs into Big D torching his family's farm, after confronting him just one short donkey ride ago:
Big D: How did I even GET here, son!?
Care Bears: Shreeky once scared Mr. Beastly into rushing downstairs. When he reached his destination, she was there to ask what took him so long and he wondered how she could be there if she was upstairs when he started coming down.
Jackie Chan Adventures: Captain Black tells Jackie not to use the phone booth, but Jackie doesn't listen and activates the secret entrance to Section 13. When he reaches the other side seconds later, Captain Black is already waiting for him.
Jackie: How did you get here so fast?
Capt. Black: The stairs.
Jade frequently appears when Jackie least expects her to. Even when he's just traveled halfway around the world.
Transformers Generation One: With a few exceptions, Autobots can't fly. When an emergency would crop in Bali or India or Japan, Optimus would yell, "Autobots, roll out!" and the heroes would drive out of their H.Q. into the desert. The scene transition bumper would appear on screen for a second, and then we'd cut to Bali or India or Japan, where our heroes have just arrived. How'd they get there? Who knows? In fairness, the Autobots in the original TV series were on good terms with most of Earth's governments, and could probably get a lift in a hurry when needed, but this is never shown happening.