Live Action Escort Mission

Our intrepid adventurer or team of explorers has been tasked with a simple mission: Get someone from point A to point B. Unfortunately, the person they are tasked with escorting is a spoiled kid or otherwise Too Dumb to Live and while they know they need to be escorted, they have no qualms against running away, going on side missions, fiddling with artifacts they shouldn't be fiddling with, making noise and attracting enemies, and generally refusing to obey the people escorting them. It can remind you of a video game.

Worse yet, the adventurers don't have the authority (or the balls) to just discipline their charge, who is a princess, diplomat, or other important figure who they don't dare upset, and whose word might be believed over their own.

If the team is lucky, the escortee will get captured or hurt, teaching them that relying on their social status to get what they want doesn't work well in the real world. If they're unlucky, the escortee might decide to Ditch the Bodyguards and go out on his own.

Exactly why anyone is willing to take such a job voluntarily without being given the needed authority over the escortee is hard to explain without Genre Blindness (or enough Genre Savvy to know it'll work out in the end). Or you were ordered to do it, or desperate, or didn't know what the person would be like, or were misled, etc.

Examples of Live Action Escort Mission include:

Anime and Manga

One arc in the Bleach anime is about Ichigo bodyguarding princess Lurichiyo.
The third Naruto movie involves Naruto, Kakashi, Sakura, and Rock Lee escorting a foreign prince and his son back to his homeland. The prince's son is a brat, and Naruto nigh-instantly gets fed up with him and tries to smack him upside the head.
- Many Naruto Filler arcs have a plot like this. It seems that every mission involves escorting a Jerkass Muggle.
Dragon Boy, the prototype one-shot that evolved into Dragon Ball, was about a strong young boy named Tanton escorting a snooty princess back to her home country. When she's not whining or insulting Tanton, she's cowering in fear of whatever comes their way.

Comic Books

Tintin, whenever Abdullah appears.
One comic starring the X-Babies, has Shadowcat "babysitting" them. Baby Wolverine is usually the most mischievous offender.
Asterix & Obelix, where the person being escorted tried holding his breath to get what he wanted. Obelix learned the same trick as well.

Film

Charles Bronson in Assassination (1987) has a scene when the first lady of the United States insists on riding in a open top convertible car. He replies that the last time the Secret Service allowed one of its "protectees" to ride in a convertible, it was JFK in Dallas...
Nicolas Cage as a Secret Service Agent tasked with protecting the former First Lady in Guarding Tess. She routinely insults and demeans the agents charged with protecting her, uses the Emergency Button like she was calling room service, and leaves the house without telling them where she's going.
This happens a lot in Indiana Jones and the Temple of Doom, although whether he's escorting Willie, Shortround, or both changes moment to moment.
The heart of Jurassic Park.
Spaceballs: Princess Vespa.
Star Wars, everywhere Padmé Amidala or Leia Organa go. Downplayed a bit, as they're both tough cookies and generally nowhere near as stupid as the classic examples of this trope.
- Not to mention Padmé has doubles.
- Not that people need a whole lot of convincing. (Since it usually involves Anakin or Han, respectively. They'd just be bored if they didn't have to shoot crap.)
This is the premise of Whos That Girl, with Madonna as the escortee.
Appears in both Conan the Barbarian and Conan the Destroyer as the reasons for Conan's quests, although the princess in the first movie barely appears and is much less annoying than the one in the second.
United 93's finale is built around a Live Action Escort To The Cockpit, but with a much more mature and serious walking MacGuffin.
3:10 to Yuma features one as its main plot, as a posse escorts outlaw Russell Crowe's character to the nearest train station, before taking it Up to Eleven at the climax, when Russell Crowe's character's gang catches up to the group.
The second half of Pitch Black.
The entire premise of 16 Blocks.
In Red Tails, the Tuskegee Airmen guard flights of vulnerable bombers over German territory in a Truth in Television example. Unlike many examples, they jump at the chance to do so, as it's the best opportunity they've gotten to prove what they can do.
In The Last Legion, the titular last legion must get the very young last emperor of Rome to Britain. The kid isn't as stupid as some other examples, but he still gets kidnapped pretty often.

Literature

This is the main plot of Michael Chabon's novel Gentlemen Of The Road. The two main characters (who are essentially mercenaries) have been asked to escort the son of a deposed and murdered king to relatives in another nation where he'll be safe, but all he wants to do is run back to the capitol to kill the usurper. Which they eventually agree to do. Also, the "prince" turns out to be a girl.
Convoy escort scenes from World War Three novels like Red Storm Rising, although in this case the merchants do have an idea what they're doing.
Subverted in the short story "Upon the King..." by Michael Gilbert (collected in Game Without Rules). A young Middle Eastern prince is being schooled in England when his father dies. British agents Mr. Calder and Mr. Behrens have the task of protecting him until he returns home to be crowned; there are elements both in and out of his country who'd like to arrange a scandal. Despite a few early bad decisions, when he catches on to the plot against him, he gets himself out of the trap before Mr. Calder and Mr. Behrens can rescue him. They, especially Mr. Behrens, are quite favorably impressed.

Live-Action TV

In the Stargate Atlantis episode "Harmony", the team has to get a princess, Harmony, to the ruins.
Inverted in the first season The Man from U.N.C.L.E. episode "The Four-Steps Affair" where Solo and Kuryakin are tasked to prevent THRUSH from kidnapping the 10 year old leader of an Asian country. The boy, far from being spoiled, is at least as (if not more) mature and worldly wise than his caretakers:

[Solo and an U.N.C.L.E. strike team have managed to free the boy lama Miki, but the leaders of the THRUSH plot to kill the boy have fled. Solo prepares to pursue them]
Miki: Wait! [Solo stops] Are those two not already finished? You know their faces. Their own organization will know they've failed. Surely they could not be running to any sort of freedom.
Napoleon Solo [looks at the boy quizzically]: Ten years old? [looks at Kuryakin]
Illya Kuryakin: I don't believe it either.

In The Greatest American Hero episode, "The Hit Car," Max and Ralph transport a gun moll to court. Unfortunately, she is seemingly a complete flake who insist of being driven to the courthouse, a journey which the heroes are repeatedly attacked by hit men where Ralph and his super suit is the only means of fighting them off. Eventually, they get the woman to court, only to have her plead the Fifth and they realize the whole gauntlet was arranged specifically to target Max.
No Heroics has Time Bomb hired to escort an obnoxious spoiled princeling

Time Bomb: Listen, I'm going to have a little sleep now so, you just wake me up when you've been assassinated.

The "diplomat" version occurs in Stargate SG-1. SG-1 is ordered to escort members of the IOA to the Alpha site. When it is overrun by carnivorous bugs, the IOA delegates demand that SG-1 continue protecting them. They do refuse to obey orders a bit at first but when they see how serious the situation is, most of them shape up.

Video Games

In Fire Emblem: Blazing Sword Erk is introduced by showing him so frustrated with his assigned escort of Well, Excuse Me, Princess! Serra he offers to refund any payment so he can just walk away. There's no Escort Mission as the deal ends before the two come under the player's control with neither needing escort (beyond what all units need due to Perma Death).

Western Animation

In Mulan 2, Mulan and Shang are escorting three princesses to meet their husbands.
One of the funniest episodes of Teen Titans was in season 5, where Raven got sent alone to escort three "younger" heroes to a safehouse from the Big Bad types trying to kidnap them. No one told her that the oldest was 4, and the youngest still in diapers. Hilarity Ensues all around. Especially when they stop for the night. Take note, when asked to tell a bedtime story she slightly dumbs down the Trigon arc into hilariously funny Nightmare Fuel for the little kids.
World of Quest is an entire series of this. Quest himself is tricked into it, the others just like Quest and think it'll be fun. The escortee, Prince Nestor, is an incompetent jackass most of the time.(Though he becomes relatively useful in fights, his ego still causes way more problems than his skills can fix, particularly since the other members of the party are still way more useful in fights.)
In the Ruby-Spears Mega Man cartoon, Mega had to escort Brain Bot, a superintelligent robot, to California. Not only did he not know when to quit messing with things and trying to "fix" them, Wily also had his sights on the brainy 'bot.