Ambiguously Brown: Heathcliff's exact race is never explained; he is referred to as "dark" and a "gipsy."
From his description as a "dark-skinned gypsy", one can surmise that he may possibly have East European/Romanian or Romani roots, due to "gypsy" (and any other variations) coming from the early West European pejorative/racist term used for Romani and East European people.
Bastard Bastard: Whether or not Mr. Earnshaw is his actual father, he has the status of a bastard; note that he has no surname.
Byronic Hero: Heathcliff is the perhaps one of the most famous example of Byronic hero: a dark, outsider antihero, lonely and demonic. He may very well be one of the earliest deconstructions, as he increasingly lacks the sympathetic side of the classical Byronic hero as he indulges in further depravity for the sake of revenge and greed.
The Chessmaster: To his credit, he manages to fool everyone to his own advantage, making him the richest man of the region without being neither a Linton nor an Earnshaw.
Dark and Troubled Past/Freudian Excuse: He was taken in as a starving orphan and then bullied by his adoptive brother (and later legal guardian) Hindley for most of his childhood. Later in his life, he makes a point of proving that anyone in his shoes would turn out as bad as him. And it spectacularly fails.
Evil Gloating: He occasionally does this to Nellie, gloating about how well is revenge is going and knowing there's nothing she can do.
Evil Orphan: He was abandoned as a small child, and he's very evil. It could also be said that said evilness could also be the product of child abuse, but it's up to the reader decide if was or wasn't he a nasty piece of work since the beginning.
Evil Uncle: He's technically Cathy's uncle by marriage, as Cathy herself notes before finding out his true colours. Also, he's again technically this to Hareton, either if he was Hindley's foster brother or his bastard brother.
From Nobody to Nightmare: Through a combination of forced marriages, alcohol and bribery, Heathcliff becomes the master of Wuthering Heights and Thrushcross Grange despite not being a blood member of the Earnshaw or Linton families.
It's All About Me: It's debatable whether he is an example of this or not, since he doesn't really care if most others are happy, but still very much gravitates around people. When he cannot center his life around being with Cathy, he starts obsessing over getting revenge on everyone.
Jerk Ass: Prone to sadistically hurting people who have nothing to do with his vengeance and enjoying it.
Lack of Empathy: He very often expresses his bewilderment at people who imagine that he will adopt a perfectly understandable and legitimate behavior towards them.
Manipulative Bastard: He easily exploits Hindley's alcoholism, Isabella's infatuation for him and Catherine (II)'s ingenuity to make his elaborate plan of revenge on the Earnshaws and the Lintons.
Masochism Tango: He and Catherine delight in emotionally hurting each other out of jealousy. In the scene in which they passionately embrace, they also delight in physically hurting each other. Heathcliff grips Catherine's arm so tightly that he leaves bruises, while Catherine tightly clasps his hair.
Meaningful Name: 'Heathcliff', which brings to mind the wild and unrestrained natural setting of the moors.
Moses in the Bulrushes: Found on the streets of Liverpool at age seven by Mr. Earnshaw and the man brought him home. At least this is what he told. Some critics have argued that Heathcliff could have very well been Mr. Earnshaw's illegitimate son, as he casually happens to find him in the streets and casually names him with a typical Earnshaw name and his wife casually takes an instant dislike for the boy.
Mysterious Past: For all of Heathcliff's life that we do know, he's still made of this trope. We don't know anything about his early years, to age seven or so, or why he couldn't speak English when he first came to the Heights or what his name might have been before that time. The mystery only deepens in the three years he spends away from the Heights and somehow has made himself so rich in that time that he's bought the house from under Hindley's nose.
Playing Cyrano: Linton's love letters to Catherine (II) are so beautifully written that it's implied they were most likely written by Heathcliff, since it's unlikely Spoiled Brat Linton would have such fantasy.
Pyrrhic Villainy: He ruins the lives of the Earnshaws and Lintons, but draws no joy from his victories and dies a bitter, empty man.
Revenge by Proxy: His plan of revenge on Hindley and Edgar contemplates degrading their children.
Scary Black Man: The 1991 edition's illustrations depict him as one, towering over an intimidated Hareton and Cathy Junior. Whilst the novel explicitly points out that he's not 'a regular black', it does repeatedly mention how sinister and intimidating his dark skin, hair, and eyes make him look.
Self-Made Man: During the three years he was missing, he somehow managed to make a fortune on his own. Given his personality and the short time he made it, it's heavily implied that said fortune is legally and morally ambiguos.
Then Let Me Be Evil: When Catherine said her Anguished Declaration of Love to Nelly, Heathcliff, who had been eavesdropping, only heard the part where Catherine says that Heathcliff would "degrade her." This prompts the embittered Heathcliff, who believed he had been rejected by the person he cared about most, to leave Wuthering Heights and disappear for three years, returning wealthy and hell—bent on ruling both the Earnshaw and Linton families.
Tragic Villain: While Heathcliff is a sociopathic monster, parts of his story are tragic. He was abandoned as a small child, adopted into a family with several members who were ambivalent about his presence, constantly treated as inferior due to his skin color and ancestry, and unable to marry the woman he longed for.
Together in Death: With Catherine. Some people can see them walking together as ghosts.
Who's Your Daddy?: Nobody knows who actually were his parents. According to some critics he may have been Mr. Earnshaw's illegitimate son.
Woobie, Destroyer of Worlds: After experiencing abandonment and discrimination throughout his childhood, Heathcliff proceeds to ruin the Earnshaws and Lintons.
All Girls Want Bad Boys: Deconstructed - the love between Catherine and Heathcliff is passionate, but it is also clearly unhealthy and intensely destructive, leading to nothing but the ruin of the lovers and almost everyone around them.
Genki Girl: At least until the residents of Thrushcross Grange get hold of her.
Gold Digger: Not that she didn't like Edgar, but blatantly states that she wants to socially elevate herself by marrying Edgar and even believes that with Edgar's money she can help Heathcliff get out from under Hindley.
Hysterical Woman: Driven to this towards the middle of the novel, going as far as searching for Heathcliff across the moors during a storm which causes her to catch a fever and die.
It's All About Me: Well, since Heathcliff is the only one she has any deep-seated interest for and she basically says she is him (and probably wants to identify entirely with him; see below), she may be a literal example. She is initially as abusive as her brother is towards Heathcliff, then manipulates Linton, doesn't care about the health of her brother, her sister-in-law, or poor Nelly, to whom she is very much a Jerk with a Heart of Jerk.
Jerk Ass: Her selfish desire to try and have everything destroys two families across several generations. Worse, she knows what both what Heathcliff is capable of and what her actions are bringing about, but refuses to change.
Love Makes You Crazy: Her love for Heathcliff is passionate but incredibly unhealthy and twisted, and eventually consumes her with insanity. Pauline Nestor's introduction to the novel argues that her desire for total identification with the object of her love ('I am Heathcliff!' rather than 'I love Heathcliff') represents a regression to childlike lack of identity, also shown by her failing to recognise her own reflection in a mirror just before she dies. Catherine's love is so insane that it basically destroys her entire identity and personality.
Nice Job Breaking It, Hero!: Her desire to have her cake and eat it (marrying Edgar for money and status while keeping Heathcliff on the side) ultimately leads to her own death and Heathcliff's descent into madness and need for revenge.
The Ophelia: As her mental health degenerates, she detaches from reality.
Raven Hair, Ivory Skin: In contrast with the blonde and delicate Lintons, the Earnshaws are described as being dark haired and robust.
She's All Grown Up: Her weeks at Thrushcross Grange, Catherine is made into a groomed and refined young lady.
Asshole Victim: If you subscribe to the theory that Hindley is murdered by Heathcliff.
Big Brother Bully: To his foster brother Heathcliff he's this since the beginning, and to a lesser extent to Catherine when she sticks to hanging out with Heathcliff.
The Bully: He bullied Heathcliff when Heathcliff was a child.
Dramatic Irony: Heathcliff's later treatment of his son Hareton mirrors the way Hindley himself treats Heathcliff when his father dies and he inherits the estate.
Dropped a Bridge on Him: Hindley's death occurs off-page but is assumed to be a result of his drunkenness. Only Heathcliff is said to be with him when he dies and it is implied that he gambles away ownership of Wuthering Heights to the latter during this period.
Drowning My Sorrows: After his wife's death in childbirth. Its also strongly implied that Heathcliff encourages this.
Badass Bookworm: Despite coming across as a nerd and a weakling, thrashes Heathcliff the one time they actually fight. Forever after, Heathcliff won't risk confronting him unarmed, even during the many long, solitary walks Edgar takes out on moors.
Love at First Punch: He falls in love with Catherine after she acts like a huge brat to the servants and even hits him.
My Sister Is Off-Limits!: With good reasons, actually. He knows very well how Heathcliff is a terrible match for his sister, but sadly she won't listen.
Nice Guy: Compared to everyone else, since everyone else is mostly a Jerkass. He's not a jerk to anyone without good reason.
Only Sane Man: The only character who isn't a dick, or an alcoholic or abusive, the one who sees through Heathcliff's plotting. He's sadly not sane enough to actively prevent most of the madness that ensues.
The Rival: To Heathcliff. It borders on Archenemy as the second part of the novel revolves around Heathcliff's plotting for Edgar's downfall, but Heathcliff never openly risks to confront him and waits for his death to take possession of his home.
Only Sane Woman: She presents herself as one of the few level-headed people in a cast of broken, vicious, and deranged characters. Upon closer inspection, she herself willingly does many of the things that she abhors in other people — such as lying to Cathy, punishing her cruelly, and keeping her captive and ignorant.
Parental Substitute: To Catherine (both of them). She was briefly one for Hareton, until Heathcliff came to reclaim him.
Horrible Judge of Character: Played with; he's inclined to think of Heathcliff as a "capital fellow" because he wants his landlord to be antisocial and reclusive. After hearing Nellie's full story, he seems to have a highly critical opinion of Heathcliff, but he doesn't do anything about it as he owes him six-month's rent.
Tellingly, he also has a very high (and accurate) opinion of Hareton Earnshaw, when everyone else considers him an uncultured lout, because he notices Hareton being torn between loyalty to Heathcliff and Cathy.
Jerk with a Heart of Gold: Unlike her mother, who is this at her best, she is this at her worst, at the beginning of her storyline and during her Broken Bird phase, when she asks for Lockwood to be lead back home, instead of let out to get lost in the swamps under the tempest.
Kissing Cousins: With Linton, as Heathcliff set up, but later falls for Hareton.
Innocent Bigot: Towards servants and social inferiors. Given her treatment of Hareton, we suppose she got better.
Spoiled Sweet: Even has some snippets of this before her Break the Haughty storyline, like when she starts taking care of Nellie when the latter is sick and she sacrifices nights out with Linton for this. Only after the aforementioned Break the Haughty does she switch to this as her default attitude.
Strong Family Resemblance: Nellie notes that although she looks nothing like Catherine except for having the same dark eyes, they are very similar in personality, particularly in their spirited and stubborn natures, although the younger Catherine's upbringing by Nellie and Edgar seems to temper her wilder impulses.
Child by Rape: This was strongly implied to be how he was conceived, since Isabella grew to hate Heathcliff, and it's implied he abused her both physically and sexually.
Dirty Coward: This is how he manages to mic his parents' worst traits, and his apparent motivation for obeying Heathcliff, but there is actually more to it. His behavior seems to be partly motivated by a genuine pleasure taken in hurting others, or seeing Heathcliff hurt them.
Two Last Names: Heathcliff isn't actually a surname, since his father is a foundling, but he has adopted this last name anyway.
Anti-Villain: He seems to be a type II-III, constantly undergoing trauma, first because of his father, and later Heathcliff, and believing the latter to have at least some right to do things as he does... He later pulls a Heel–Face Turn for Cathy.
Berserk Button: Don't insult Heathcliff in front of him. Cathy eventually learns it's a lost cause trying to change his perception of Heathcliff.
Create Your Own Villain: Arguably, Heathcliff tries this on him as a way to prove that, in the same conditions, anyone would have been as bad as him. It fails miserably, as weirdly enough Hareton developed positive feelings for him and most of all has the gentle nature he has never had.
Crush Blush: He blushes and strongly denies to be Cathy's husband.
He Cleans Up Nicely: Despite Heathcliff best efforts to make him dirty and unrefined, it's evident he's good hunk material with his strong build, broad shoulders, dark hair and dark eyes.
Foil: For Linton Heathcliff and to a lesser extent Heathcliff himself.
Hidden Depths: He seems to carry Heathcliff's spirit, as becomes an ignorant, dirty and uneducated man, but he has the gentle heart Heathcliff will never have a thing that makes Heathcliff's plan for him fail miserably.
Like a Son to Me: Heathcliff grudgingly admits to like Hareton more than his own sickly, spoiled son. Had the boy not been Hindley's son, he'd like to have a son like Hareton. This doesn't quite stop Heathcliff from mistreating Hareton as his revenge contemplates.
Love at First Sight: He's instantly smitten with Cathy (II) but it takes years for her to notice and like him back.
Love Redeems: Cathy's love helps him rise above his circumstances.
Made a Slave: Heathcliff raises him as a crude, illiterate servant-boy.
Meaningful Name: He's named after the Hareton on the main door, which is obviously the ancestor of the Earnshaws. He's the one who starts a new beginning for the family.
Never Learned to Read: Until Cathy starts to teach him, leading to the two bonding and Heathcliff eventually losing the will to continue his vendetta.
Parental Abandonment: Is largely left to his own devices by Hindley Earnshaw after his mother dies. Nelly cares for him for a while, but then Heathcliff decided the boy was his business...
Slap-Slap-Kiss: Almost literally with Cathy (II). Their bickering becomes more and more benevolent as they grow fond of each other.
Stockholm Syndrome: Heathcliff manages to make Hareton look at himself as his only friend and father figure. Wow.
Tsundere: Rare male example. Especiallytowards Cathy. Because of his disadvantaged childhood and an abusive Parental Substitute he has not learned how to properly express his feelings, so he could be a sweety one moment and then send you to hell if he feels threatened.