Adrian Mole: Adrian is almost this to Pandora in the early books, after they break up as teenagers (and Pandora eventually marries another man.) In The Cappuccino Years he acquires his own Stalker with a Crush, Eleanor Flood.
The eponymous antagonist of Terry Pratchett's Wintersmith, who falls in love with young witch Tiffany Aching. In an attempt to win her heart, he makes snowflakes and icebergs that look like her and ice roses... and oh yeah, he refuses to go away when it's time for spring, creating the threat of perpetual winter.
Robert B. Parker's private detective Spenser picks one up in Hush Money. After dealing with a stalking case for Susan's friend K.C. Roth, Spenser finds that KC has started stalking him.
Severus Snape was a Stalker with a Crush for Lily Potter (nee Evans) even when they were children, although she liked him once she noticed him. They remained friends until he started hanging out with Voldemort sympathisers, she tried to warn him against them to no avail, and he called her a Fantastic Slur. Add to that her choosing to marry Snape's school rival James and Snape unintentionally setting Voldemort on her tail, which got her killed...
Merope Gaunt has been stalking the handsome Muggle Tom Riddle for days before her family found out. They didn't take it well. Later, she bewitched and married Tom and the two of them became Voldemort's parents
Lanfear in The Wheel of Time acts this way towards Rand, the reincarnation of her old lover. Upon first meeting him (in disguise) she flirts heavily, then a few books later she pursues him, aiding him in learning The Power, but then tries to kill him after she hears a rumor that he slept with someone else.
Also Raoul de Chagny, to a lesser extent; he fixates on Christine Daae after having being apart from her for years, constantly tries to gain her attention, and even goes so far as to listen at her door and hide in her dressing room.
Mr. Darcy spends a few early chapters of Pride and Prejudice following Elizabeth around in public, staring at her, and eavesdropping on her to the point where Elizabeth is slightly creeped out. When they're both staying in Kent, he stalks her favorite place to walk in the park and spends entire evenings at Rosings staring at her but never speaking to her. This doesn't stem from any malicious intent, however; it's just that Darcy is so socially inept, he has no idea how to act when falling in love.
A more malicious Jane Austen example is Henry Crawford of Mansfield Park, who persists in tormenting the object of his desire (Fanny) no matter how much it distresses her.
Ricky Lozada from Sandra Brown's The Crush. In fact, the book's title is referring to Lozada's stalker crush on Rennie Newton. He constantly watches her, breaks into her house multiple times (leaving roses and later trying to "seduce" her), and has his geeky subordinate check up all the information he can on her.
Edward Cullen from Twilight falls under this trope quite well, except that Bella returns his affection. Some examples of Edward's stalker behavior are sneaking into Bella's house at night to watch her sleep without her permission, taking the battery out of her car so it can't run, and stalking (and then saving, so it's okay for him to stalk) Bella. No matter how much Stephenie Meyerdenies it, he's most definitely a stalker.
This is taken to even more ridiculous extremes in the parts of Midnight Sun that were leaked - it seems that for nearly every chapter of Twilight when Edward wasn't around, he was actually hiding in the bushes, spying on Bella. It also lets the readers see his thought process, so everyone is privy to him thinking to bring oil the next time he climbs into her room so the window won't squeak and reassuring himself that what he is doing is all right because it's for her own protection.
Fenwick from Villains by Necessity is a womanizer to begin with, but when he spies Kaylana among the villain protagonists, he immediately decides that he must save her (and give her a personal tour of his quarters) because she's attractive. Doesn't sound creepy? While his constant spying is explainable as keeping tabs on the villains' progress, he obsesses over her presence in specific far more than professionally required. And then resorts to kidnapping her. By dragon.
Zane from Mistborn has an unhealthy fixation on the heroine, Vin, because she's the only person the voices in his head never told him to kill. Vin, for her part, treats Zane more as a Not So DifferentWorthy Opponent, but isn't romantically interested in him at all, preferring his less Badass but far more stable half-brother Elend. When she finally says "no" to him, Zane tries to kill her, being a psychopath and all. It doesn't work out so well for him...
Warrior Cats: Spottedleaf spends the first series stalking Firestar, and still watches over him afterwards. Additionally, she also stalks each successive generation of his family. Although, Firestar does love her back, and it is a somewhat popular shipping; in spite of him also truly loving Sandstorm, who he fathered kits with (Leafpool and Squirrelflight).
If you consider every single thing the author has said as Word Of God, then Spottedleaf is officially a stalker.
In The Hellfire Club by Peter Straub, the villain Serial Killer Dick Dart acts like one towards Nora. He latches on to her due to a misunderstanding that she had kidnapped and tortured a woman, which caused him to believe that he finally found his worthy match and someone who was just like him. As a result, he kidnaps her and repeatedly rapes her, taking her along as he commits crimes all the while thinking of her as his accomplice. When she escapes from him, he stalks her and kidnaps her again, actually admiring her even more for managing to trick him.
The Sheik of The Sheik, who doesn't even bother to stalk his intended very long before outright kidnapping her. 'Crush' might be a bit of a misnomer, though; he just wants to rape her. Which he does.
Z For Zachariah has a stalker with a something; Loomis is a little too intent on hunting down Ann, for multiple reasons, only one of which is the fact that he wants to rape her. His sanity is a little questionable as well.
In the Nero Wolfe story "Murder is Corny", model Susan MacLeod asks her farmer father to hire a man she's casually dating. After she dumps him she finds out that he'd lied about needing a second job - he only wanted to force her to spend time with him. He eventually tells the other men she's dating that he's made her pregnant in an attempt to force her into marrying him to save her reputation. The story, which is false, seals his doom.
In The Pillars of the Earth, After William Hamleigh seizes the Shiring Earldom, he is aware that Aliena, Richard and their servant Matthew are still living in the castle. He stalks and watches over Aliena with freakish fascination, still obsessed with her even after she disgustedly rejected him twice. As soon as he gets the chance, he rapes her.
"But thou shalt be my queen, oh princess! I will teach thee the ancient forgotten ways of pleasure. We—" Before the stream of cosmic obscenity which poured from the shadowy colossus, Yasmela cringed and writhed as if from a whip that flayed her dainty bare flesh.
Frederic/Ferdinand/Caliban from The Collector by John Fowles starts as one, but unlike many, goes past this phase, actually abducts his flame, and proceeds to...well, not exactly torture or rape, but rather "keep" her.
The protagonist of the short story "We Love Deena" by Alice Sola Kim is this trope incarnate.
Caelan from the Skulduggery Pleasant novels. He spends his days spying on Valkyrie through her kitchen window.
Dr. Ahriman of Dean Koontz's False Memory has a brief bit of this. He mind rapes most of his patients and uses them for all kinds of things, be it murder, revenge, or just... entertainment. He winds up (kind of) legitimately smitten with one, fortunately not realizing this until she and her husband have skipped town. By the time they get back, they've broken his mental hold and he winds up murdered by another patient.
Arguably, Goethe's poem "Der Erlkönig" (The Erlking/"elf-king"). The Erlking follows a father and young son traveling through the forest. Apparently invisible and inaudible to the father, he tempts the increasingly terrified child to come with him, offering him games and pretty clothes. When pretending to be nice doesn't work, the Erlking just uses force instead: "Ich liebe dich, mich reizt deine schöne Gestalt/Und bist du nicht willig, so brauch ich Gewalt" ("I love you, my youngling; your form is so fine/And will you or no, I'll still take what is mine"). Right after this, the child screams that the Erlking has "hurt him," and he dies in the next stanza. It may not have been intentional, but to the modern reader the poem radiates this trope.
Some characters (and a small minority of readers) take Michael’s behavior towards Angel in Redeeming Love this way. Although his methods of contacting her are entirely legitimate, he continues to romantically pursue her even after she vehemently denies wanting anything to do with him. In-story this is Justified by the fact that he’s trying to rescue her from life as a Stepford SmilerSex Slave.