Delayed Causality

—Kenshiro, Fist of the North Star

A Dramatic Pause used for action scenes. The hero (or villain) punches his foe. Dramatic Pause... and a giant explosion obliterates him. Or, the hero swings his sword. Dramatic Pause... object/opponent falls to two pieces. This is not like using a Time Bomb, where a delay is deliberate. This is ignoring the laws of physics for the sake of dramatic effect. For all intents and purposes, the attack was over when the punch landed... the resulting effect simply decided to wait a few seconds before showing up.

The Delayed Causality is almost always used in a Single-Stroke Battle.

The target of the attack doesn't have time to, or simply won't, react to it until the final explosion occurs. The only reaction, if there is one, is to acknowledge how the opponent bested him before he dies.

The can also be used simply as a display of skill. For example, hero throws a block of wood into the air and slashes a few times. The wood block falls down... Dramatic Pause... and breaks apart into the shape of a peacock.

Examples of Delayed Causality include:

Anime & Manga

Hayate the Combat Butler, when Isumi destroys the Koi Herpes Virus.
Parodied in Dragon Ball: Mr. Satan pays no. 18 to take a dive in their tournament match. Mr. Satan punches 18, who is completely unaffected. She asks Mr. Satan whether that was his most powerful attack, and he says yes. She jumps backward off the arena, and the audience misinterprets it as a Delayed Causality punch.
Claymore just loves this trope.
In Code Geass, this happens in the fight between the Knight of One and Suzaku
Saint Seiya loves this one. Foes don't drop dead until they realize they've been hit.
Frequently played straight in Yu Yu Hakusho. In what was possibly the earliest example in the show, Hiei slices an opponent something like sixteen times; said opponent has time for some gloating before he finally slides into pieces.
In Japan, that pause where nothing is happening is called "Mu", something like "emptiness". It's important as a punctuation in Japanese theatre and is used most famously (to the point of being parodied in countless other anime and manga) by Goemon Ishikawa XIII in the Lupin III series. Goemon even has a Catch Phrase that he says before the items he has just cut fall into pieces: "Again, I have cut a worthless object."
Fist of the North Star. That is all.
In One Piece this is Brook's signature fighting style.

Comics

Subverted in this strip of the French comic Game Over: the protagonist gets the time to retaliate... not that it does any good.
- Played straight here.
There is an issue of Sin City where Miho slices her sword across a mobster's wrist. There's a moment before the hand falls off where the mobster is looking down, wondering what just happened.

Films -- Live Action

In Cube, one of the rooms slices up a character with Razor Floss but the pieces don't fall apart for a few seconds.
In Equilibrium, The Dragon to the Big Bad is on the receiving end of one of these.
Towards the end of the first Underworld movie, Seline does this to Viktor when she slices him in half with one swing. There's a pause, he's still moving as though he's alive, then he falls apart.
- Parodied by How It Should Have Ended: "Wow. I thought his head was never going to fall off."

Literature

Done in one of the Honorverse prequels to a hexapuma.
Shagga, son of Dolf claims his axe is so sharp that he once cut off a man's head without the man realizing it until he went to brush his hair. Tyrion muses that this is why Shagga never brushes his.

Live Action TV

Justified and Played for laughs in Red Dwarf, when Lister and Rimmer are under the effects of a time-manipulating device, so when two bruisers start pummeling them, it doesn't have any effect... until several hours later, when they're in the captain's office and suddenly start getting beaten and tossed around by thin air.

Video Games

Yojimbo from Final Fantasy X's Zanmato.
StarCraft II has a cinematic sequence where Zeratul cuts off one of Kerrigan's blade-wing things. It takes a few seconds to fall off.
Most heavy attacks in Super Smash Bros Brawl send foes flying a few frames after they connect.

Western Animation

This happens in some form or another in almost every episode of Samurai Jack.
- Also occurs in Star Wars: Clone Wars, the animated micro-series from Jack's creators. Ventress does it to her final opponent in Count Dooku's "tryout".
In Wakfu, Sadlygrove's sword slashes often go according to this, but similarly often split stuff immediately too. Rule of Drama applies. Exhibit: Dream Sadlygrove slices up the dragon monster in Evangelyne's dream sequence in the Sadida Tree of Life.