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Francis Underwood from the US version of House of Cards as well the majority of the cast. In fact, the Arc Words of the series are "choose power over money" showing that those character motivations are not typically Greed but are in fact this.
A couple of Disney villains have this as their primary motivation.
Scar murdered his brother and attempted to kill his nephew in order to rule Pride Rock.
Ursula manipulated Ariel in order to get Triton's trident, which would let her rule the seas.
Jafar in Aladdin manipulated the Sultan and tried to forcibly marry Jasmine in order to become Sultan himself. He throws in a bit of lust for Jasmine herself once he got the power he desired.
Lust for Sex
Anime and Manga
Happosai, in Ranma ½, could practically be considered the Patron Saint of Stealing Women's Underwear and Lecherous Old Folks. He's over a century old (three centuries in the anime), and has been stealing lingerie, ogling women, groping women, and chasing tail since he hit puberty. He's such a pervert that he actually gets weak and sickly if he can't regularly admire a bra or touch a woman.
The 1998 miniseries Merlin provides a particularly interesting example in King Uther. His Fatal Flaw, and his doom, is his lust for Igraine, the wife of the Duke of Cornwall. To satisfy his desire, he goes to war against the Duke, causing the death of hundreds, eventually kills him, and with Merlin's help, rapes Igraine by deceit. After he's satiated his desire, however, he has no more interest in her, and simply leaves her and the bastard child he'd begotten (Arthur). Over time after the incident, Uther slowly slips into madness until he is almost The Caligula before he finally commits suicide. At the same time, his killing of her father enrages Morgan le Fay, who later becomes a pivotal enemy of Merlin and Arthur.
Pick any version of Robin Hood. Chances are that either the Sheriff of Nottingham or Guy of Gisborne will lust after Marian.
In Neil Gaiman's adaptation of Beowulf, it is the titular Beowulf's weakness for beautiful women that allows Grendel's mother to manipulate him so easily (though oddly, the tagline of the film was "pride is the curse").
Balthamel in The Wheel of Time originally became evil so that he could indulge his sexual lust with reckless abandon.
Ditto Rahvin, who uses mind control to force women into having sex with him, since he can't handle rejection.
Graendal too. She was actually celibate before her Face-Heel Turn, but now she regularly holds orgies.
In Cloud of Sparrows, Zephaniah's first point of view scene is a detailed description of his lust for Emily.
C. S. Lewis explains in The Four Loves that the difference between Lust and Romantic Love (eros) lies in "his attitude to her five minutes after fruition (one does not keep the carton after one has smoked the cigarettes)."
Also from C. S. Lewis is The Horse and His Boy. The second half of the book's action is based on a Calormene Prince's lust for Queen Susan, who uses this as his excuse for invasion.
In Lolita, Humbert is motivated by his lust for, well... Lolita the young Dolores.
Brian de Bois Guilbert in Ivanhoe. Though nominally a Knight Templar (not a Knight Templar, though), he stalks and tries to rape the Jewess Rebecca. In the end, during a Duel to the Death he dies of a heart attack, likely not because Sir Walter Scott minded having the hero kill him but because he wanted the poetic justice of having the villain killed by his own lust.
In the 1980s American cartoon, Ganon's motivations for kidnapping Zelda sometimes included getting his hands on her, as well as the Triforce of Wisdom. Of course, this may just be part and parcel of his unending lust for power.
Sir William the Black from Overlord is a fallen paladin-turned-cult leader who has spent most of his recent time ignoring the deaths of the people in Heaven's Peak to satisfy his own carnal desires.
Sector Bootes from Shin Megami Tensei: Strange Journey. The entire subdimension is modelled after a red-light district, with a huge central tower nicknamed in-game as the "Palace of Pleasure". It is, however, also home to a fair number of Mad Scientist demons, who express an obscene lust for knowledge.
Drip the sin of lust in the Furry WebcomicJack is motivated by sexual desire mixed with a lust for power and causing pain. When alive, Drip was a murderous serial rapist.
Judge Claude Frollo from The Hunchback of Notre Dame (the Disney film - in the novel, Archdeacon Frollo isn't a true villain) is a pride-focused villain at the beginning of the story, but when he sets eyes on the gypsy Esmeralda, he is consumed by his lust for her, and decides to have her executed when she refuses to go along with him. The Disney movie has her narrowly escaping being burned at the stake, but the original Victor Hugo novel gets a lot grimmer — she's hanged for murdering Phoebus, who is in the crowd, uninterested in coming forward (since he's a Jerkass).
Coupled with the blatant racial and religious bigotry plotlines, can you believe it only got a G rating?
In the original book, Captain Phoebus was more of a case of lust, what with the womanizing ("while" engaged to someone he spends most of the book seducing). But Archdeacon Frollo could still counts - he's not truly a villain, but by the end he's so unhinged and/or desperate he'd rather get Esmeralda hanged than have her refuse him.
Anime and Manga
Lust for respect is one of the main flaws of Light Yagami in Death Note; it combines with his pride to generate a severe god complex. The only time Light shows a strong emotion (besides when he's defeated by Near) is when he feels L humiliated him.
In Umineko no Naku Koro ni, the youngest sister of the Stakes of Purgatory is Asmodeus, who represents the sin of Lust. However, it is stated in her TIPS that she desperately wants to fall in love. If those around her don't fall in love and simply give in to their lusts, it increases her vice.
General Raven, one of Father's pawns, also suffers from lust, for sex and power, but most of all, for more life. He's an old man whose time is running out and he cuts a deal with Father in the hopes of living forever.
Ironically, the final moments of the homonculus Greed implies what he wanted more than anything was to have friends, which is desiring an abstract concept. Similarly in the 2003 anime, Greed's ultimate desire was to be free of his creator, either by outliving or killing her.
In the 2003 anime, Lust's motivation is an intense desire to be human.
Ren Kouen from Magi - Labyrinth of Magic lusts after knowledge. He claims to care about his empire, but his brothers Kouha and Koumei know he just conquers as many lands as possible in case they have the answers he's looking for. After meeting Aladdin, he agrees to fight a horde of monsters just to get a chance to talk with him, and in the middle of said fight, his mask of calmness cracks and he slaughters everything in his path for the sake of that chat.
BlazBlue's resident Bishounen Jin Kisaragi has "Lust SIN" as his musical theme. Though, if this is referring to his obsession for killing his older brother or something else remains to be seen. On another note, Hazama/Terumi manages to mix Lust with Wrath and Envy - he is prone to torturing people not just to mold them for his own twisted plans, but in many cases just because he feels like it. While there is some justification in that he requires people to acknowledge his existence in order to persist (getting people to hate him is easier for him), the level of excess he takes it to (which also mixes this with Gluttony) is just plain disgusting. He even shows rather violent 'withdrawal' symptoms, as he screams loudly whenever he loses a torture victim (he really hates Rachel over this) and is willing to kill whoever interferes if they stick around (see Jin and Makoto). And this is not ALL Hazama entitles, he's actually fits allSeven Deadly Sins.
Each of the villains in the Keys to the Kingdom series represents a deadly sin, with Lady Friday representing lust. To be precise, lust for human memories and experiences. She seems to be addicted to them, and routinely kidnaps senior citizens (who have had more experiences) and drains them of all their emotions. They never wake up again. If the experience is deemed too "impure" (in a quality sense, not anything else), she discards it and gives it to a subordinate.
Lilithmon, one of the Seven Great Demon Lords is the personification of lust. True to her name, she's sultry, seductive, wears a rather exotic outfit, and has one of the largest set of breasts in the franchise, rivalled by Angewomon (who is an archangel and yet ironically even more Stripperific), Venusmon (AKA the Digimon counterpart of Aphrodite/Venus, the Greek/Roman goddess of love and mad hot sex), and Mervamon. Naturally, she lusts for many other things, including power.
Slaanesh is the god(dess) of it in Warhammer 40,000. The actual subject of the lust doesn't matter — it is the extreme desire that fuels Slaanesh.
Andrealphus is the Demon Prince of Lust in In Nomine. He mostly (and enthusiastically) focuses on sexual lust, believing that Love Hurts and is a weak thing as a result, but also covers all other areas of intense desire.