Basic Trope: Someone (usually of royal blood) begs a sovereign to have the hero spared from execution or another unpleasant fate.
Straight: Princess Carol begs her royal father to spare Bob from execution.
Princess Carol grabs her father's ermine cape, collapses to her knees, and wails for the king to not dock Bob a half day's pay for serving tea that wasn't hot enough.
Princess Carol travels to the gods' abode and begs the king of gods to not throw Bob to hell.
Downplayed: Princess Carol begs her royal father to spare Bob from a traffic ticket.
Justified: Princess Carol cares about Bob, and Bob certainly doesn't deserve to be executed. The logical course of action would be to appeal to her father, who has the authority to spare Bob.
It is a Civil War and Bob was on the losing side. Princess Carol believes magnanimity to be good politics.
The princess begs for Bob's execution.
The Princess begs Bob to spare her father.
Bob begs the king to spare Princess Carol.
The king begs Princess Carol to not callously execute Bob.
Princess Carol promises Bob she'll try to get her father to spare his life, but when the time comes she demands that he be executed.
Princess Carol begs her father to spare Bob knowing exactly that, because of her action, the father (who is a tyrant and a Slave to PR) will execute Bob.
Princess Carol's father orders Bob beheaded. Princess Carol begs her father not to behead Bob. But then she reveals what she wants done instead: dip Bob feet first into molten lead, because she's really a lot madder at Bob than her father is.
Doubly Subverted: Princess Carol promises Bob she'll try to get her father to spare his life, but when the time comes she demands that he be executed. Oddly, the king spares Bob's life anyway; as he's being led out of the throne room, Carol murmurs to him, "My father always has been susceptible to Reverse Psychology..."
Parodied: Princess Carol does this everytime her daddy says she can't have something.
Zig Zagged: Princess Carol promises Bob she'll try to get her father to spare his life, but when the time comes she demands that he be executed. Oddly, the king spares Bob's life anyway; as he's being led out of the throne room, Carol murmurs to him, "My father always has been susceptible to Reverse Psy--" and then they fall into the Shark Pool. Which is empty— turns out the king knew about terrorists planning to assassinate both Carol and Bob if he didn't execute them. But the terrorists knew about the Shark Pool gambit and work for the king anyway. Which is why they don't kill them.
Averted: Princess Carol merely gasps and despairs as Bob's sentence is announced.
Enforced: "How are we going to realistically get Bob out of this execution? Oh! We have to give Carol a Pet the Dog moment anyway, so let's have her persuade her dad to pardon him!"
Lampshaded: "Wow, Princess Carol, if all you had to do was ask, why'd you wait 'till the last minute?"
"I'll sentence Bob to death. That will Break the Haughty for my daughter; she will beg for him to be pardoned."
"Just sparing Bob would not impress my clemency on the crowds; they'd just assume he wasn't that bad. I'll condemn him to death, and you plead for his life, Carol. That'll not only make me look good, it will convince people to come to you if they're too scared of me."
Defied: "I am not getting down on my knees like some shameless beggar! I'll just have someone break you out in secret."
Discussed: "Get down on your knees and have him spare Bob, princess! Kings are always suckers for noble beggars!"
Conversed: "The king is so uncompromising? What does it take: getting down on their knees and kissing his damned feet?!"
Princess Carol's begging makes her father look down on her for acting as though she were a beggar allied with some commoner. He disowns her.
The king, touched by Carol's begging, pardons Bob. Bob was every bit as dangerous as the king thought, and promptly raises an army, overthrows the king, and kills him. Bob lectures Carol about the folly of mercy to your enemies before killing her too.
Reconstructed: The whole thing is a Secret Test of Character for Princess Carol. Her impassioned pleas convince the king that she truly cares about the wellbeing of people other than herself, and as a result the king makes her his heir and allows her to marry Bob.
I swear, father, they will look at the tropes if you let them go, I'm not just saying that, he is very loyal to people who do him a service, but Please Spare Him, My Liege!