Code Geass: First Prince Odysseus U Britannia (a nice guy compared to the rest of his mostly ruthless, brutal, cunning, sadistic, racist, and downright assholish kin but not very bright for the heir apparent to Britannian throne) almost had an Arranged Marriage with Token Mini-Moe Tian-Zi, the Empress of China. Obviously, it was not meant to be.
Gundam SEED Destiny: Yuna Roma Seiran. Foppish, tactless and supremely arrogant, Yuna was so unlikeable that fans actually wished Cagalli had just shot him on the spot during their first meeting. Super Robot Wars K tries to moderate this somewhat, with some limited success.
The noble title of Conrad in Rune Soldier isn't entirely clear, but he has all the traits of the trope. He's even much more worse at being a hero than Louie, who at least has the spirit to help people and shows some degree of competence, while Conrad is just an Upper-Class Twit.
Hotohori from Fushigi Yuugi has some shades of this trope, mainly because he hasn't learned to interact informally with people due to his sheltered existence, and also because he's more than a little vain. He's actually very nice, and he means well, though.
Kagerou of Inu X Boku SS. He's not a literal prince, but he is the heir to a wealthy and influential family and is the arranged fiance of the main heroine. His outrageous behavior completely betrays any prestigious upbringing you'd expect him to have and does nothing to endear himself in his fiancee's eyes. He is extremely hammy and rude, has an incessant need to create a Big Entrance for himself, and compulsively categorizes literally everything he sees into being either a Sadist or a Masochist.
Zig-zagged in The Slayers. Lina Inverse was seeking out to meet Crown Prince Philionell of Saillune, thinking he's the typical Prince Charming, to charm him into marrying her. When she encountered him, she found out that he's a boorish man more fit to be a bandit chief, and old enough to have a daughter not much younger than Lina. But it turns out Phil is a nice guy after all; Lina's matrimonial plans shatter, but she still befriends Philionell. Phil's daughter, Princess Amelia, even becomes a permanent member of Lina's adventuring party.
To help clarify, he has a natural ability that makes people instinctively like him, but after a time it no longer has an effect; by the time he first appears in the story, he's managed to charm his way into and subsequently get chased out of every royal and noble house in Europe.
Gaston also qualifies as this, despite not being an actual prince (more like an Alpha Male). He's self-absorbed as well as a big Jerkass to everyone in town, including Belle, who he is trying to get to marry him.
The trope namer is Prince Paul from "The Secret of Anastasia". Taken a bit further than most examples. He's not a prince at all - he's actually the ruthless Secret Policeman Checka, who murdered the real Prince Paul and is posing as him to romance Anastasia, steal the Romanov fortune, and dispose of her.
Just Ella: Prince Charming in this Cinderella retelling.
A Song of Ice and Fire. At first, idealistic young Sansa Stark believes Joffrey to be a Prince Charming and is greatly looking forward to their arranged marriage—but after things go to hell and she becomes a prisoner of war at King's Landing, she quickly realizes Joffrey is a total sadist and her life with him will be far from happy. She still has to keep up the facade of loving him, lest her time at King's Landing become worse...
It should be note that Joffrey is very capable of appearing charming when he wants to. He just doesn't like doing it, so the pretense is permanently dropped as soon as he's crowned King.
In By the Sword by Greg Costikyan, the princess has great misgivings about her Arranged Marriage to one of these princes. The prince is fat, smelly, and has bad table manners. The princess eventually talks to a member of the prince's court, who explains that the prince is actually a very gentle man, and he's also extremely gay, so the princess never has to worry about having to have sex with him. She is reassured by this, and decides that this marriage won't be so bad.
Therandil in the Enchanted Forest Chronicles (on purpose, since it's a Deconstructive Parody). Most of the princes in the series are like this. It's implied that most of them mean well, though, and—like princesses—were just given "traditional" upbringings which resulted in their silly behavior.
Played with in The Paper Bag Princess; Prince Ronald is clearly this, and Princess Elizabeth realizes this at the end, but there's no lower-class equivalent for him. So she dumps him and lives life alone—played as a Happy Ending.
Chronicles of Prydain: Prince Ellidyr is not at any point set up to be the heroine's love interest but otherwise fits the trope perfectly. And given that the heroine is a princess while the hero is a commoner, it's not a reach to understand why the hero was a little nervous about the possibility of such a match arising anyway.
Prince Rhun was—at first—this trope played straight. Although not malicious, he was an obnoxious bumbling manchild and The Millstone to any group saddled with him. There was talk of betrothing Eilonwy to him in the future, and Taran was disgusted and furious at the thought. He was never as stupid as Taran initially thought, however, and he did do some growing up.
Discworld: The Duc in the novel Witches Abroad. He's not technically a prince but the principle applies. He's in cahoots with evil fairy godmother Lilith, and Magrat is called in (with Granny Weatherwax and Nanny Ogg along for the ride) to save Emberella from marrying him.
Young Queen Selenay is swept off her feet by one of these, only to realize too late what a mistake she made. The Heralds keep silent rather than let her know that they have misgivings about the match, since they don't have any proof to back things up and outright trying to forbid the marriage would just make her more insistent on the marriage, and it nearly backfires fatally when the Prince and his friends try to assassinate Selenay.
His brother, Prince Darren, starts off as one of these but eventually learns sense.
Prince Ancar of Hardorn, who attempts to marry Selenay's daughter, is one of these at best: then he throws off the mask and shows what a monster he actually is.
A tricky variation in John Moore's The Unhandsome Prince. The titular Prince Hal is not this trope, but Caroline doesn't want to marry him—the reward for kissing the right frog is supposed to be a handsome prince, and Hal is...well, not the thing girls dream about. His oldest brother, Prince Kenneth, on the other hand, seems like all Caroline could ask for, except for the rudeness, the arrogance, the mean streak, the cruelty to animals, the utter ruthlessness...
In "Prince Charming", Princess Anastasia is afraid her young brother, Dmitriv, might actually be this for Vasilisa. Lazy, irresponsible, and a flirt, Dmitriv doesn’t look like the best match for the good-hearted Vasilisa. Subverted in that Dmitriv resolves to make a change for the better by the end.
Prince Ghyaneth of Berringey in Elemental Blessings. He's blunt, rude, Berrincentric, and his country practices routine regicide of every royal save the heir to ensure there are no factions or coups. Princess Josetta can't stand him.
Live Action TV
Alice: In this SyFy mini-series, Jack Chance is first seen as a normal, decent, Nice Guy when he proposes to Alice, until the Reveal mid-way, where he is shown to be Prince Jack Heart, the Big Bad's son. Also a Rebel Prince in a previously Arranged Marriage, helping Alice and the Wonderland Resistance to overthrow his mother. Later gets hit with a case of Wrong Guy First when Alice rejects his second proposal and hooks up with Hatter.
Into the Woods: Both Princes. They're clearly just after "hard to get" girls and lose interest after they've gotten them. Cinderella's prince cheerfully seduces the Baker's Wife into a quick fling, and at the end, both guys have moved on from Cinderella and Rapunzel to Snow White and Sleeping Beauty.
Portia's suitors in The Merchant of Venice. There's a scene where Portia and Nerissa consider them then dismiss them all. Only the Princes of Morocco and Aaragon get through to the casket lottery, but even then the Spaniard's usually portrayed as Ambiguously Gay and the Moroccan is usually played like he's on jehad. Of Course Bassanio's the only one for Portia.
Dragon Quest V: Prince Harry. When you first meet him, he's a six-year old selfish prankster who only cares about himself, offering you to be his lackey (only to say you're not worthy of being one), and even complains about how long you took when you and your father come to his rescue. After Pankraz's death and being enslaved by the Order of Zugzwang for ten years, he gets better.
His son, however, ends up being a carbon copy of his dad during the spoiled-brat phase, even going so far as to pull the same stunts on the main character's own children, though thankfully without any kidnapping occurring.
Dragon Quest VI: Prince Howard of Howcastle, who goofs around with village kids and forever runs from the cave of trials that every heir to the throne has to go through by a certain age. It takes no less than three false starts before the party finally drags him through the trials. However, the experience obviously impresses upon Howard the magnitude of the task, and he buckles down once the quest is completed.
Psychonauts has Dingo Flagrente (AKA Dean LaGrant), a Jerkass Matador existing in the mind of Edgar Teglee who supposedly stole his love Lampita (AKA Lana) from him, according to Unreliable Narrators. When Raz meets the more Reliable Narrators, the story is clarified as Dean stealing Lana from him.
In Warcraft Prince Arthas appears to be a classic good and noble hero. He's a paladin for the Light's sake. However, the game and particularly expanded universe materials reveal not only his slide into darkness, but the fact that really? He was already a bit of a jerk. The paladins (other than Uther) never really liked him and make sure to point this out just before he kills them.
In Puzzle Quest: Challenge of the Warlords, the player character has the option of helping Princess Seraphine run away from an arranged marriage to one of these.
A straighter example in the same game is the Jerkass that was bespelled into a frog. At least his frog crown is useful.
King's Quest VII also has a little of this, though only in passing. Although we never meet the prince in question, the intro features Valanice trying to talk Rosella into marrying one of the princes of another kingdom, who Rosella claims is "sooo boring".
In Fairy Godmother Tycoon, one of the rival potioneries is the NSHP, or Not-So-Charming Princes. As the story progresses, they turn out to be nice fellows.
Play your cards right, and they will marry Cinderella's Ugly Stepsisters (They're sweet while Cindy's a spoiled brat)
No Rest for the Wicked: Prince Ricardo AKA "Dick the Picky". The words "Picky" and "Dick" pretty much describe his personality completely.
He's something of a Grammar Nazi, and the Princesses he rescues tend to be somewhat ditzy.
He also gave up on Sleeping Beauty because she snored. That is to say, rather than at least wake her up, he just walked out the way he came in, leaving her to her eternal sleep. In an unassailable castle no one had ever gotten into before. Nice move, Dick.
Legend of Zelda: Prince Facade was so excessively concerned with appearances that he was willing to let Zelda get kidnapped instead of risking getting his clothes dirty.
My Little Pony: Friendship Is Magic: Ever since "The Ticket Master," Rarity had hoped to meet "him," Princess Celestia's distant nephew Prince Blueblood. It is not until "The Best Night Ever" that she finally meets him in-person during the Grand Galloping Gala. Unfortunately, Blueblood turns out to be a vain, stuck-up jerk, and after he uses Rarity as a pony shield against a flying cake, she finally gets fed up and chews him out for it.
To clarify the full significance of this: Rarity has always been shown to be a very dedicated social climber. Blueblood is so intolerable she's willing to completely torpedo her own reputation to dress him down properly.
Not a prince, but in episode 3 of Scooby-Doo! Mystery Incorporated, Daphne's parents push her to go on a date with a snobby rich guy. He's late to the date, won't stop talking about himself, steals Daphne's food, and makes her pay the check. Needless to say, she ditches him real quick.
In The Simpsons Treehouse of Horror episode "Wiz Kids" the class is practicing "standard toad-to-prince spells". Milhouse's incantation is "slimy prince limey". That alone should be an indication of what kind of man the frog turned into. It should be noted, however, that Milhouse's Prince was head and shoulders above Bart's attempt.