Abusive Parents: He dotes on Mary and Elizabeth...until his marriages to their mothers dissolve, at which point he strips them of their legitimacy, banishes them from his court, and occasionally toys with the idea of having them killed.
His extreme protectiveness is also a form of abuse to Edward, as Jane Seymour points out in her season 4 cameo. Granted, this time Henry really tried to do what he thought was best for him.
Adaptational Attractiveness: Not at first, since Henry actually was considered very attractive in his youth. Trouble is, he stays that way even through the period when Henry became obese.
Ass In Ambassador: The man is a walking diplomatic incident, constantly either insulting foreign dignitaries to their faces or capriciously deciding to renegotiate treaties at the drop of a hat.
Chronic Backstabbing Disorder: On both a micro scale (the best way to tell that you're about to be executed is to have Henry come to you and reassure you of your position in his court) and a macro one (he constantly breaks his treaties with France and the Holy Roman Empire).
Control Freak: Oh, my, yes. As Cromwell realizes (too late) in Season 3, this is the true reason why he began the Reformation: he has no particular theological disagreements with the Catholic Church, he simply won't countenance the idea that someone, somewhere in England might ultimately be under the authority of someone who isn't him.
Kill 'em All: If you rebel against him, you will pay dearly for it...
Ladykiller in Love: Subverted. The closest he comes is with Jane Seymour, if only because she both gave him a son and died when their marriage was at its apex. It didn't stop him from having affairs. Afterward, he marries purely for political reasons.
The series implies, especially in the series finale, that Anne Boleyn was his great passion (particularly in that he doesn't want her ghost to leave him). But to say that he truly loved any of his wives is really... dubious.
His failed marriages are always someone else's fault, usually the unlucky wife's.
He convinces himself that the apparent deformity of Anne Boleyn's last child is ironclad proof of her (nonexistent) adultery, since obviously the kid must be someone else's.
After the deaths of Wolsey and Cromwell (and the discovery that they were pretty much his only competent advisors), he lays all the blame for their departures on the rest of his Privy Council. While it's true they had a hand in Wolsey and Cromwell's downfalls, it's also true that they would not have occurred if Henry hadn't decided to get rid of them for his own reasons.
Pet the Dog: His last meeting with Suffolk might seem like a Kick the Dog, because he's basically dragging a dying man out of bed to go see him, but it's still a nice moment between him and his Only Friend. He even offers to use his "powers as king" to cure him of his fever. Sadly, it doesn't work.
Villain with Good Publicity: Within England, certainly. No matter what bastardly things he does, his people are always willing and even eager to blame his advisors (Wolsey, Cromwell, Cranmer, and Anne Boleyn being favorite patsies).
Foil: To Henry, in so many ways. Henry starts off as a promising, dynamic monarch, but quickly becomes Drunk with Power and becomes a tyrant. Charles starts off a wastrel who ignores the duties of his office, but undergoes Character Development and becomes the king's most loyal, capable, and reasonable servant, and a powerful magnate. They start off being very similar personalities, but end up being very different.
Not So Different: Infidelity is a constant problem with both of them. Charles makes a conscious effort to be faithful to his second wife, until Catherine makes it clear the two of them will never reconcile. Henry does who he wants, when he wants, and doesn't give a damn what any of his wives think.
Genre Savvy: He lasts the longest in Henry's court, and is one of the very few characters to die a peaceful death. Henry notices, after a while, that Charles surreptitiously disappears from court when Henry is particularly enraged, like after Katherine Howard's execution.
A Match Made in Stockholm: In Season 4, he falls in love with a Frenchwoman who was his prisoner during the Boulogne campaign.
My Greatest Failure: Putting down the Pilgrimage of Grace. He considers it a grievous moral failure on his part after he sees thousands of people killed, and Thomas Darcy brutally executed, all because Cromwell threatened him with censure. He's much more subdued afterward, his marriage is destroyed, and his friendship with the King is not as close as it was before. When he returns to Pontefract Castle, he's visibly affected, and starts glimpsing Darcy's spirit wandering the halls.
My Master, Right or Wrong: He angsts about what this entails. In Season 3, his oath to Henry drives him to commit actions against his better nature.
Noble Top Enforcer: None of Henry's other advisers would be satisfied with executing only the leaders of a rebellion, while sparing the thousands of ordinary rebels.
Older Than They Look: Cavill's Brandon looks perpetually boyish, whereas the historical Brandon was actually seven years older than Henry VIII. During the Boulogne arc in season 4, Brandon looks forty at most when he would have been nearing sixty.
Reasonable Authority Figure: Eventually. Case in point, contrast his leadership of the English army at Boulogne, with Henry's. Also, at Surrey's tribunal following his military blunders in France, Charles is the only one who actually addresses the charges at hand. Thomas Seymour and Bishop Gardiner are more interested in slandering Surrey with false charges of corruption. Later, when the two are speaking privately, Charles assures him that his punishment is not damning, and that if he keeps his nose clean, he might one day regain his glory on the battlefield.
The Rival: He eventually becomes a second center of power on the Privy Council. When his rivalry with the Boleyns becomes public, his retainers and Thomas Boleyn's retainers start fights on the streets of London. When Thomas Cromwell tries to assume leadership of the Privy Council while the grieving Henry is incommunicado, Charles leads the other lords in walking out and shutting down the government, forcing Henry to return and neutering Cromwell's influence.
Butt Monkey: Everyone except Henry hates his guts and plots against him, and Henry slowly becomes convinced that he is deliberately blocking his divorce from Catherine (even though the exact opposite is, in fact, true).
Dangerously Genre Savvy: When it came to the politics of Europe and the court, Cardinal Wolsey could play the game like no other.
Can't Get Away with Nuthin' : The one time he lets his personal feelings override his Yes-Man tendencies (when he pushes Henry to marry Anne of Cleves in order to cement an alliance with the Protestant League), it ends up getting him executed.
Karma Houdini: Subverted if you know your history, as he would die just two years after the events of his final episode, having been made bankrupt and lost everything he and his daughters had fought for throughout the series.
Kick the Dog: In his final episode he is informed of Anne Boleyn's impending execution. His response? To ask whether he can keep his earldom.
Overt Operative: While on assignment to abduct or assassinate Cardinal Pole.
Remember the New Guy: The real Bryan was actually a major player in Henry's court throughout his reign, but the character never appeared in the first two seasons. When he finally shows up in Season 3 as Henry's closest aide, everyone just acts like he was always there.
Full-Circle Revolution: Under his leadership, the Reformation in England grinds to a halt and the reformers that enjoyed widespread patronage under the Boleyns and Cromwell found themselves targeted for investigation, torture, and execution.
Age Lift: The real Earl of Surrey was in his late twenties during the events of Season 4. David O'Hara was 44 at the time of filming.
Anti-Villain: He's entirely right about Hertford, Gardiner, and Richard Rich being schemers, and his friendship with Suffolk shows he's not a bad guy. But after he tried to kidnap Prince Edward, there was only one way it could end.
Irony/Hypocrite: He's extremely dismissive of the "new men" populating Henry's court, but his only friend at court is Suffolk, who was made Duke without an ancient or celebrated lineage. Charles looks uncomfortable every time Surrey rants about the importance of lineage, and tries to gently remind him of the worthwhile service people like the Seymours have rendered the King, Blue Blood or not.
Small Name, Big Ego: Once she starts actually throwing her weight around at court, it becomes glaringly obvious that she has little intrinsic political worth. Henry's advisers, for example, bristle whenever she voices her objection to the king's policies, and when she can't bear Henry a son, Henry tires of her and has her executed.
Genre Savvy: After the lesson of what happened to Henry's first two wives, she's sure to immediately agree when he asks for a divorce, enabling her to make out quite nicely on the deal and even retain his favor afterward (the real Anne even attended the coronation of Mary).
Justified in that Katherine Parr is a strong Protestant and therefore (to Mary's eyes) an Affably Evil heretic at best.
Jumping Off the Slippery Slope/Knight Templar: Toward the end of Season 4, she lets her hatred of the "heretics" consume her, vowing to restore England to the "true faith" no matter how many people she has to burn to do it.
Too Good for This Sinful Earth: The series finale foreshadows that despite Henry pinning all his hopes for the Tudor dynasty on him, he will die young like his mother.
Princess Margaret (Gabrielle Anwar)
Composite Character: Henry VIII had two sisters, Margaret and Mary. The show keeps the name that would lead to less confusion with his daughter Mary.
Continuity Snarl: Henry's only having one sister in the show, who dies childless, makes Henry calling the King of Scotland his nephew in season 3 rather inexplicable. In real life, of course, this is because he was the son of Margaret, whose own story was removed (the show's Margaret has the rough biography of the sister named Mary).
Sinister Minister: Downplayed, but definitely there, as when he not-so-subtly encourages the assassination attempts against Anne Boleyn.
The Spymaster: He founds the Jesuits to act as his operatives abroad.
Tempting Fate: He allows Henry's appointment of Thomas Cranmer as Archbishop of Canterbury because, as he puts it, "What harm could a nobody do to our Holy Church?"
Charles de Marillac (Lothaire Bluteau)
Advertised Extra: He gets billing in the opening titles, despite only appearing in five out of ten episodes and only appearing for a scene or two in each. (This is probably because the show was an Irish/Canadian co-production, and Lothaire Bluteau is a fairly big star in Canada.)
Ass In Ambassador: Played with. He is scrupulously polite and servile to Henry, but the claws come out whenever he and Chapuys are alone together.
The Generic Guy: Doesn't really get enough screentime to develop a personality of his own.
Catherine Brandon, Duchess of Suffolk (Rebekah Wainwright)