Code Geass: First Prince Odysseus U Britannia (a nice guy 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.
Comic Books
Fables: Prince Charming is this to Snow White. And Sleeping Beauty. And Cinderella. And almost Beauty. Yeah, he gets around. Eventually he does turn his life around and is killed saving the world.
To help clarify, he has a natural ability that makes people instinctively like him, but after a time it no longer has an effect, he managed to charm his way in and get chased out of every royal and noble house in europe when we first see him.
Sweet Home Alabama: While not a literal prince (although probably pretty close with being the son of New York City's mayor), this was the intended role of Andrew Hennings. Unfortunately, they made him too likeable compared to the other side of the Love Triangle.
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.
Prydain Chronicles: 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. Like Farquaad above, 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.
And he's a frog.
In The Royal DiariesCatherine The Great Journey by the time Catherine married the weak Man Child Peter III Of Russia he was disfigured and once he ascended the throne his loyalty to his country of birth ruined Russia's successes in the Seven Years' War.
The Prince in Roald Dahl's Revolting Rhymes is downright Ax Crazy, cheerfully chopping the heads off the ugly sisters before they can try the shoe on. Cinderella marries a jam-maker instead.
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.
Theatre
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)
Webcomics
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 Ticketmaster," 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.
As the ponies are fleeing the gala, Rarity drops a glass slipper...and when Pinkie Pie points this out, smashes it out of fear he'll use it to find her.
