Convenient Misfire

Guns, like any machines, are prone to malfunctions; the most common, and thus the most likely to pop up in fiction, are jams and misfires. However, since there's no good reason for a gun to jam in the middle of a straightforward firefight, expect any errors to come during a crucial moment.

You can also think of it this way: does this gunshot have the power to end the plotline? If yes, and if the plot isn't at its actual end, it's fairly likely that it won't go off quite right.

Of course, when real guns jam or misfire, it's fairly easy to fix (depending on the gun and the era, of course.) That said, if it comes down to timing, a misfire or jam may make or break a gunfight. It's also much more common in period pieces, as modern weapons are much more reliable than, say, 19th century revolvers.

May overlap with Shur Fine Guns. Similar to My Car Hates Me.

While the title of this trope is misfire-specific, do note that it applies to any type of failure to work on the gun's part.

Examples of Convenient Misfire include:

Anime and Manga

In Full Metal Panic: The Second Raid, Xia Yu Lan's gun jams while she's trying to kill Kaname. She quickly and methodically clears the jam and resumes firing, averting some other tropes associated with gun jams, but the momentary reprieve saves Kaname's life.

Comic Books

In Le Tueur, the killer's gun misfires right as he's about to kill himself with it. Of course, once he's fixed it, the suicidal urges have evidently passed.
In Knights of the Dinner Table, Bob accuses Brian who is GMing of doing this to save BA's and Sarah's characters when Bob's character's gun misfires during a gunfight in a Cattlepunk game. Bob points out that the character's gun is a cheap revolver that's just been submerged in a horse trough.
Tintin's life is saved by this several times, including one with a cannon.

Film

Aversion: in The Way of the Gun, Longbaugh's shot gun jams in the middle of the shootout. Instead of editing around it Benecio del Toro clears the jam and keeps firing.
In Back to The Future, Marty is saved repeatedly from being shot by Libyans because their rifles keep jamming. They are shooting AK-47s, which, in Real Life are famed for their reliability even under the harshest conditions.
During the Mexican Standoff in Pirates of the Caribbean: At World's End, it turns out that none of the guns work because they all got wet, thus conveniently avoiding having to kill off four main characters at once.
Unforgiven. William Munny enters the saloon where Little Bill Daggett and his deputies are celebrating the death of Ned Logan. He confronts Little Bill and prepares to kill him for torturing Ned Logan to death. Watch it here.

Little Bill: All right, gentlemen. He's got one barrel left. When he fires that, take out your pistols and shoot him down like the mangy scoundrel he is.
Munny: [Points shotgun at Little Bill and pulls the trigger] Click.
Little Bill: Misfire! Kill the son of a bitch! [Gunfight begins]

Averted in Get Shorty. Ronnie is not intimidated when Bones points a gun at him because he states the model is notorious for always jamming at the wrong times. Bones promptly shoots him four times rapidly.
Man on Fire features this when the main character attempts suicide, but the gun misfires. He takes it as a sign and gives up on the idea.
The Mexican revolves around this.
A scene in Schindler's List in which a Nazi officer attempts to execute a Jew, but his pistol misfires. He calls over another soldier to execute the Jew, but his pistol misfires as well. They give up on the idea. Due to the nature of the story, this was probably based on a real incident.

Literature

Author J. T. Edson disliked it when guns jammed or misfired for no reason in movies, so whenever it happened in his novels he would give a detailed explanation of what caused the gun to jam. That said, it still happened several times when it was convenient for his heroes. The short story Jubal Branch's Lucky B.A.R. was one example.
In Les Misérables, policeman Javert is standing facing Thenardier, who is holding a gun. Javert tells him not to shoot, since the gun will misfire. Thenardier shoots at point blank range and the gun, predictably, doesn't go off.

Live Action TV

In CSI: Miami, Speedle's nearly killed when his weapon jams from lack of cleaning. He doesn't learn his lesson and gets Killed Off For Real when it jams again.
Averted in War of the Worlds. Actor Richard Chaves (playing Lt. Col. Paul Ironhorse) had his assault rifle jam during an action scene. Being a Vietnam veteran, Chaves just cleared the jammed blank as he would a real round and kept firing.

Video Games

Call of Duty Black Ops, in the Khe Sanh mission, has Woods almost getting killed but for the player's intervention when his gun jams right before he kills an NVA soldier. He tries fixing it by whacking it a few times.
- Also, in the multiplayer, to prevent people from using modded controllers, the semiautomatic rifles will jam if fired too fast.

Western Animation

The episode "Harlequinade" of Batman: The Animated Series originally ended with one of these, where Harley Quinn has a machine gun pointed at the Joker (because just was pissed that he was willing to let their pets die in his latest scheme). Joker makes it clear that he doubts she has the guts to shoot him, but she does... only for a flag reading "RAT TAT TAT" to pop out, to her surprise. According to the commentary, originally there was simply going to be a click, but the flag was added to soften the blow.

Real Life

President Andrew Jackson survived an assassination attempt when both of the would-be assassin's pistols misfired. Interestingly, both pistols were examined and determined to be in working order. Daniel O'Brien guesses "that the bullets, like everyone else, were simply scared of Jackson."