Contrived Coincidence / Phineas and Ferb

• In every episode, the eponymous young boys build a spectacular creation and Heinz Doofenshmirtz builds an invention of evil. Whenever Doofenshmirtz loses control of his invention, no matter how far away it is, it will inevitably destroy, directly or indirectly, any evidence of what Phineas and Ferb built that day before their mother can see it (much to the bafflement of their sister Candace). Less often, Phineas and Ferb will do something that seems inconsequential at the time but actually helps their pet platypus Perry (who's a secret agent) defeat Doofenshmirtz later on. One or the other (or both) happens Once per Episode. Perry the Platypus is the only one who's aware how much the characters affect each other's lives on a daily basis.
• In addition, the two subplots are always near each other. Phineas and Ferb are on a trip to see Mr. Rushmore? Doofenshmirtz's base is in Mt. Rushmore! Phineas and Ferb are visiting their grandparents in England? Doofenshmirtz is attending an evil convention in England! Phineas and Ferb are in space... (That one got semi-lampshaded.)
• When they build a super computer it takes advantage of the coincidences to let them do the nicest thing possible for their mother, fixing her hair after a horrible hair day. The computer even gets a Literal Genie moment but it is Made of Explodium, all things it anticipated.
• Then there are the even less likely moments where Perry's two dual lives meet, such as when Dr. Doofenshmirtz takes his girlfriend to the restaurant Phineas and Ferb built in their backyard, or when Candace delivered girl scout cookies to Doof's apartment, while Perry was still there. Jeremy once went to Doof's home to teach him how to play the guitar. Doof once dated Linda. He once went to a garage sale at the Flynn-Fletcher household. (It's not known if he knows Linda lives there.) It goes to the point where every character has interacted with the doctor at some point, bar Phineas and Ferb themselves, and they have gotten close at points.
• Averted in Phineas and Ferb The Movie: Across the 2nd Dimension, where the boys land in Doof's building, destroy the machine (an "Other-Dimension-Inator"), and then cheerfully help him fix it. And then Perry busts in, freezes when he sees them, and attempts to stop the doctor in 'mindless pet mode'. He fails. They travel to another dimension, and then gets outed as a secret agent, but then Laser-Guided Amnesia (literally, they get zapped with a laser that erases memories) allows the characters to press the Reset Button and forget all about it.
• The same Phineas and Ferb The Movie: Across the 2nd Dimension has both Perry and Candace invoke the coincidence to save the day. Perry knows the boys can build incredible things, and has been saving all of their disappeared inventions for use by the boys, along with their friends and allies, to defeat Alternate-Doof's invasion. When it's still not going well, Candace forces their mom out to see what's happening, reasoning the "Mysterious Force" preventing her from busting her brothers, now that they are involved due to their saved inventions, will clean up the entire city. She was right.
• In "A Real Boy", Candace finally gets Mom to see Phineas and Ferb in the middle of their big project for the day. As luck would have it, Doofenshmirtz accidentally hits himself with his "Forget-about-it-inator" (it makes you forget about whatever you're thinking about at that moment), then pulls a "What Does This Button Do??" and erases Linda witnessing the project...several times in a row, no less.
• In the episode "Don't Even Blink", the characters decide to watch the boys' latest invention to see where it goes. On the day where Doofenshmirtz has built an invisibility ray. Every time Linda comes to look it goes invisible, and it turns visible again when she leaves... and when Candace realises you can still feel it, her attempt to cover it in paint is thwarted by Doof deciding to screw the whole thing, and convert the machine to a disintegrator ray.
• Many of the patches that the Fireside Girls earn are conveniently linked to Phineas and Ferb's project of the day, but this is justified. They have Merit Badges for Everything, and the local troop leader has such a crush on Phineas that she's earned the "help your neighbor" patch alone dozens of times just to spend more time with him.
• This unfortunately doesn't apply when it comes to Candace's own projects. In situations where the boys are protected by random chance, Candace is not and will be caught every time.
• In "Rollercoaster: The Musical!", Phineas and Ferb make a new rollercoaster just like the original from the series' first episode and Doofenshmirtz tries to revert Earth's rotation the same way he tried back then.
• In the crossover episode with Milo Murphy's Law, it's revealed that they have a power that is basically the opposite of Murphy's Law.