MythBusters deconstructs this trope. They demonstrate what is possible and what is not.
Buffy the Vampire Slayer states that only one slayer can exist at a time; when one dies, the next awakens. That's what the Council decreed. The show skirts this trope with clinical death which creates two slayers, but doesn't fully play it straight until Willow decides to break the rule and wake up EVERY possible slayer.
Warp 10 is said to be the highest warp and it is; the only thing that increases is the speed of Warp 10. However, no matter how fast it becomes, it's still Traveling at the Speed of Plot and therefore not really changing at all.
Star Trek: Voyager in the episode in which the warp ten barrier is introduced. Voyager reaches Warp 10 and exists at every point in the universe, but also causes the humans on board to evolve into salamander-like creatures. The episode has since been officially disowned by the writers.
There were two distinct warp scales used in Star Trek. The one that was used in original series was a cubic function (velocity = warp factor cubed x the speed of light) and had no upper limit. The one used from Star Trek: The Next Generation on is hyperbolic and made warp 10 equal to infinite velocity—even if you were traveling at warp factor 9.99999..., you would still be infinitely far from warp factor 10 in this scale. There was yet another warp scale used in All Good Things... and the future version of the Enterprise travels at Warp 13 on this new scale. Some of the Expanded Universe materials attempt to rationalize Warp numbers as being the most EFFICIENT speeds where there's a dip in the energy output needed to sustain the speed.
The characters of Deep Space Nine are used to a Mirror Universe where they exist as brutal yet sexy version of themselves, but in the last mirror episode "The Emperor's New Cloak" Quark and Rom witness the death of Vic Fontaine — despite the fact that Vic is not a real person but a fictional holodeck character in their universe. After trying to puzzle this out for a while, they just give up.
Pawn Stars: Rick buys a car for Old Man's birthday and needs it restored. It's estimated that it would take 6 to 8 months to restore the car, and that's if Rick the restorer didn't have any other jobs the entire time. Rick needed it in three, and somehow, it was done in three. While Rick's shop worked on other projects.
Seinfeld: Parodied as part of Jerry's ridicule of Kramer's claim that Keith Herandez spat on him. He traces the imaginary path of the spittle which involves changing directions and pausing in mid air. "that is one magic lugee." The point being to illustrate how impossible it was for the event to happen in real life.
Xena: Warrior Princess features numerous Gods, (of Greek, Norwegian, Turkish and Roman orgins, among others) which like any Gods, are immortal. This is a universe where Immortal Life Is Cheap. For the first five seasons, it doesn't matter what you did to a god, they would not die. However, in the Season 5 finale, Xena gains the power to "Kill the unkillable." In the span of 12-15 hours after gaining this power, Xena had killed Poseidon, Hephaestus, Deimos, Hades, Artemis and Athena, with no signs of slowing down.
Xena also features the title character being impregnated by the redeemed soul of her archenemy, Callisto. When she discovers she is pregnant, she expresses the impossiblility of the situation, by slamming the doctor into a wall.
After it had been made clear that it could never happen, Rose reappears in the same dimension as The Doctor in "Turn Left." There's only one possible explanation: All reality is falling apart.
The moment you take your eyes off of one of the Silence, you completely forget about them. River wasn't just shooting something she couldn't see, she shot something she literally could not have known was there.
The Doctor can scare the Daleks, who are supposed to be physically incapable of feeling any emotion, fear included.
The Doctor also directly changes his past timeline, though as Rory puts it, "To be fair, the Universe did explode."
There are many things about Eleven's companion, Clara, that are impossible. For instance being in more than one time and place at once, being killed in both, and showing up a third time. The way time travel works in Doctor Who should make it impossible for both Oswin and Clara to exist, and yet they do anyway.
Everyone is limited to their own personal sphere of Heaven unless they are soulmates or their name is Ash who discovered a means to hack Heaven and walk between the difference spheres, for the express purpose of partying with famous figures from history.
The only thing that can kill an angel is another angel, but then without so much as saying anything about it, it becomes possible with one of their swords. This is justified because their swords are manifestations of their Grace, which is what gives them the power to kill each other.
Their reaction to to setting fire to a car-wash, which is made of "90% water".
Being the first humans in history to drive across the Makadikadi Salt Pans as well as to the North Pole!
Level Up: The weapon needed to kill Maldark is supposed to kill the heroes using it with its recoil. This information comes straight from the creator of Conquerer of All Worlds, Max himself. The heroes survive it and he is shocked.