Character Development: Obviously, nowhere near as well-designed or thorough as the books, but it's pretty evident here. Taran goes from an impulsive kid fantasizing that one day he will be a hero, to a more mature, compromising young man who realizes he is unfit to be what he considers a hero.
Failure Knight: Taran so wants to be a Knight In Shining Armour, but at almost no point in the film does he successfully do anything useful with his own skills: He loses Hen Wen almost immediately after being entrusted with her; when held captive by the Horned King he only escapes with the help of Eilonwy and the magic sword; and he unwittingly brings the Black Cauldron into the Horned King's hands by getting it from the witches with whom it probably would've been completely secure (as well as giving away the potentially story breaking magic sword in the process). At the end of the film, Taran actually acknowledges that he's a failure as a warrior and forfeits his chance to become one in order to resurrect Gurgi.
Adorkable: He has shades of this, especially when he's reduced to nervous sputtering.
All Thereinthe Manual: The book explains why Fflewddur's harp keeps breaking and how he got it, and includes the detail that he's not really a bard at all, but a king who left his kingdom to become a bard, and failed the academy.
Badass: At the end, when he uses the witches' creed against them.
Batman Gambit: Fflewddur completely ruins the Witches' Batman Gambit, reminding them that if they will repossess the Cauldron, they must make an exchange of equal value back to the heroes.
Butt Monkey: In the course of the movie, he's captured, has his pants torn by dogs, falls into a pit, and is turned into a frog.
Cloudcuckoolander: At first, he appears to be so. Visit an ominous, gloomy castle that looks so obviously suspicious nobody goes there? Hey, you're a bard, why not? He later proves to be much smarter than most would give him credit for.
Chick Magnet: One of the witches is dangerously attracted to him.
Foil: To Taran. Whereas Taran is more hotheaded, ambitious, and headstrong, Fflewddur is more of a Shrinking Violet.
In the book, Taran and Fflewddur were much more alike.
Foreshadowing: The witches proclaim that "What we do is bargain, trade!" Fflewddur later throws these words right back at their faces.
The Load: Poor Fflewddur was much more useful in the book. But alas, he only proves useful twice - weakly trying to convince the feuding Taran and Eilonwy that they have to work together, and taunting the three witches into trading the restoration of Gurgi's life for the return of the Cauldron.
Mood Whiplash: In a very dimly lit scene, the Horned King orders for his pet dragon-lizard-things called Gwythaints to hunt down the heroes who have escaped from his gloomy castle. Directly following that is Fflewddur singing a silly song.
Dangerously Genre Savvy: Decides its better to have Taran and co to find the Cauldron for him and then chains them so they don't escape like last time. The only reason he failed was that he failed to take into account Gurgi, someone that never that went into the castle and would have no idea about.
Dem Bones: Has a skeletal appearance is reduced to one during his death.
Non-Action Big Bad: He spends most of the movie standing still and doesn't really get very involved in any of the action. When he does tangle with Taran in the movie's climax, he loses almost immediately.
No Sense of Humor: What makes him so menacing. Out of all other Disney villains, even Maleficent could spare a sarcastic laugh or two.
Our Liches Are Different: It's not clarified if he is a lich or a hideously deformed man, but it's clear from his powers and aura that he's not entirely human to say the least
Skull for a Head: The Horned King is a horned variation. While he's an undead evil sorceror, the rest of his body looks quite normal compared to his positively skull-like head.
Sorcerous Overlord: The Horned King, although his magical powers are fairly limited and require complex rituals to realize. This tyrant is a horned, robed member of the undead, probably a lich. He plots to take over the world from his fortress by acquiring an army of skeletal warriors known as the Cauldron Born.