Combat Uninterruptus

Alice and Bob are fighting. Carol enters with a message for Alice, who calmly carries on a conversation just as if Bob character weren't trying to kill her. Usually used to demonstrate just how much more Badass Alice is than Bob, but if she kills Bob without taking notice, it can also show disregard for life.

Related to Dissonant Serenity. For a "make love, not war" version, see Coitus Uninterruptus. Compare Kinda Busy Here, when the messenger is on a phone.

Anime and Manga

 * Dragonball Z: Taken Up to Eleven; King Kai and Guru are telepathically discussing a plan to move everyone on Namek to Earth. Then Goku, in the middle of his fight with Frieza, interrupts them, telling them to leave him on Namek to defeat Frieza.

Comic Books

 * Done in Zot. Zot is fighting two thugs while Jenny berates him for selling out.
 * A Running Gag in PS238 is that, whenever almost anyone phones The Revenant, he is busy fighting some supervillain or other and calmly carries on the conversation while fighting.

Film

 * Under Siege: The hero is in a ferocious firefight with the villains when he gets a satphone call. He takes the call while blasting the baddies. This example does use the trope to add humour to the proceedings by having Ryback's Sidekick initially take the call as though she were a bad PA: "Is Ryback there?" "I'm sorry he's in a gun fight right now. Hold on I'll put him on for you."
 * Used brilliantly in Grosse Pointe Blank, with John Cusack blasting a houseful of assassins to death one by one, while conversationally exploring the meaning of his own existence and declaring his love for Minnie Driver's character.
 * Played for laughs by Cary Elwes in Robin Hood: Men in Tights, from Mel Brooks.

Live Action TV

 * In Buffy the Vampire Slayer, in the first part of season 3's finale, Buffy hands Giles a newspaper article about a murder while he's practicing fencing with Wesley. Giles effortlessly parries all of Wesley's advances with one hand and almost no attention.

Tabletop Games

 * If there were such a thing as White Veil Style, it would have this as one of its central abilities.

Video Games

 * Used in the first Osu! Tatakae! Ouendan game in the Salaryman stage. Our hero receives a phone call in the midst of battle with a giant mouse. Failing to perform well here actually means he gets his ass kicked, while passing this portion plays the trope straight.

Web Comics

 * This Girl Genius page is particularly illustrative- one character does it and, seconds later, another one does something that would be it if he hadn't only just arrived.
 * In The Adventures of Dr. McNinja, Dr. McNinja does a variation of this at one point; the Doc calls Gordito and the clone of Ben Franklin on his cellphone while fighting ninjas, and at one point one of the ninjas grabs the phone from him.