Tomoyo Daidouji is this, as mentioned in the Anime and Manga section of Stalker with a Crush, but it gets taken massively out of proportion in some Fan Fiction. For Example, in thesechaptersof Takamichi Nanoha of 2814, she hires a team consisting of Deathstroke the Terminator, David Cain, Deadshot, Tatsumiya Mana, and Lady Shiva to guarantee the safety of her crush, Sakura. As well as ordering illegal nuclear weaponry and carries around two "Lex-Blaster 500s". All of which turn out to be worth it during the confrontation with the Big Bads during chapter 10. Going even beyond that she started a religion based around worshiping Sakura.
The Moriarty clone's behavior ragarding Beth Holmes in Children of Time is largely this. He outright admits to Beth's husband, Sherlock Holmes, that he's been keeping an eye on her (while she was in Death Seeker mode) to ensure that she'll remain a Worthy Opponent. On the whole, he tends to address Beth more than he does Sherlock (and with Terms of Endangerment), apparently as part of his mind games.
In Forward, the Academy agent named John is strongly implied to be one of these towards River. Made even creepier by the fact that, while he really does care about her, his goal is to bring River back to the Academy so they can continue to Mind Rape her to make her "better," and he is convinced that this is the right thing to do.
Flippy is usually portrayed as this in fanfiction. Most stories involve Flippy and Flaky, in which Flippy either rapes Flaky or kills her while she is terrified of him and tries to get rid of him. In the cartoon, the situation is pretty similar, because Flippy has killed Flaky many times, but when he acts nice to her, she is afraid of him and runs away... or stabs him.
In Ginny Weasley's Future Husband Ginny has a "Harry Potter box" filled with everything from partially-clothed photos of him to some of his boxers and admits in public that she made a statue of him in her bedroom.
Romilda Vane in A Question of When is obsessed with Harry Potter, to the point that when she somehow gains the power of Mental Time Travel at some unspecified point in the future, she goes back in time not to save the Wizarding World... but to try and convince Harry that they would be perfect together. She spends countless lifetimes Save Scumming to try and figure out the best way to seduce him and ends up accidently rewriting reality along the way.
Obsidian in Some Semblance of Meaning. Instead of practicing with weapons in the Training Center (not that he needs to), he stands around and watches the other tributes... and takes special notice of ValeWhitaker. Later, after they have gone into the arena, he locates Vale and her district partner while they're asleep, but instead of killing them, he just watches them for a brief time, takes a pair of laurel crowns Vale wove, and leaves them be. And the next day, he shows up there again and makes sure Vale sees him this time and, again, doesn't harm her. This makes her feel very paranoid, but he actually does have good intentions and isn't portrayed too negatively for these actions, and although Vale does notfind stalking romantic, she does come to return his feelings eventually.
Becoming Ponies example: Pinkie Pie encounters a rather enthusiastic woman who she's okay with letting stroke her mane. Once the woman starts making sexual advances, however, she is thoroughly creeped out.
In MLP: The Games We Play, Rainbow Dash finds herself stalked by one of her friends disguised as Mare Do Well. The catch? She doesn't know who it is, so Mare Do Well makes the pegasus a bet; that Mare Do Well will be able to get Rainbow Dash to fall in love with her before Rainbow Dash can discover her true identity. The result is some kind of hybrid romantic mystery/psychological thriller.
In the Pony POV Series, Sergeant Thunderchild (Shining Armor's Number Two) claims to fall in love at first sight with Fluttershy, despite only ever having seen pictures of her. Shining and Cadence both call him out on how creepy it is. Interestingly enough instead of stalking her at the Wedding, once the Changelings are defeated, he simply asks her on a date.
Sophistication And Betrayal has a completely serious example when Rarity ends up being stalked by Slate, which is portrayed as being as extremely upsetting and creepy.
Naruto fanon's stalker supreme is Hinata Hyuga, and this is practically canon. Its one of the few facts that Naruhina and Narusaku fans agree on, its just how they depict this, as either endearing, or creepy, that sets them apart.
Chapter 14 of Rorschach's Blot "What If" collection of Naruto oneshots titled "I Did It, My Way" has Hinata as a Stalker With A Crush who breaks into Naruto's apartment to take hair from his drain, steals his clothes (while leaving new things for him), and breaks in occasionally while he's asleep to strip him down and measure him so she can buy him new clothes. He takes this in stride, believing it to be the work of the "Clothes Fairy". It's played for laughs, and is far from the weirdest part of the story.
Chihiro Tanaka and other Shinji's female classmates started chasing him obsessively, looking for excuses to spend time with him or chances to flirt with him, trying to have lunch with him or walking with him back to his house... Shinji has made clear that he does not want the attention but they will not stop.
Asuka also had to put up with a horde of boys chased her even though she made her disinterest clear and blunt. However, since they refused to take "no" for an answer she scared them away most efficiently so that everybody took the hint. She explained this to Shinji in chapter 8:
Shinji:' "Maybe that will finally get them to stop chasing me like I'm a prize to be won. [...] How come I'm the one with the pack after them? You were ten times as popular as I was, a week after you arrived, miss incredibly-hot-exotic-foreign-transfer-student. I know Touji and Kensuke were making crazy amounts of cash selling beauty shots of you almost right away. Why haven't I had to chase away a pack of boys drooling after you?" Asuka: "Because I already had them properly terrified and respectful after I mashed the first two flat when they tried to ask me out the week I got here and refused to take 'no' for an answer, [...] Putting a couple of them on the ground with a few punches when they got rough taught the others to keep off. You're just too polite and sweet to girls to scare them off, my darling baka."
Evangelion 303: Saburo is trying to get Kaworu back using all means that he can think of. However his antics are managing the opposite effect, and Kaworu is beginning to actively dodge him.
HERZ: Kurumi to Shinji. She has been chasing him since they met in high-school, and she is unable to take a "No" for answer. She even got him drunk and slept with him several years ago, and even though he got married she has flirted with him, has thrown herself naked at him, has blackmailed him to kiss herů and he always refuses -or runs away-, but she never listens.
Baker School Blitz has this as a consequence of Jim being obsessed with Mr. Lestrade. Lestrade doesn't go into too much detail, but he did have to change his number a few times because of it, something that unnerves John.
Bart Simpson Attorney At Law: JessicaLovejoy for Bart, having learned that the kid hellion has become a successful attorney. Not caring about the stress she is causing Bart, she declares him to be hers. Then she begins badmouthing Alex, following him around, and demanding his whereabouts from his co-workers. She evolves into full-blown Yandere by kidnapping Bart and trying to drug him into saying a marriage vow.
Ultimate Spider-Woman has a particularly twisted version in Ronald Hilliard, a teenage boy who's a guest at a high-class party that's attacked by Spider-Woman's Arch-Enemy Jack O'Lantern. When Mary Jane Watson goes into action as Spider-Woman to protect the party guests, Ronald gets it into his head that she was there to protect him specifically. His crush on her then drastically escalates, as he goes from wallpapering his bedroom with images of Spider-Woman and turning it into a combination Room Full of Crazy and Stalker Shrine to her, to spending his entire $5 million trust fund on gaining superpowers. As the Psycho Electro Supercharger, he begins murdering Spider-Woman's detractors as a means of proving his affection for her. He culminates in full-on Yandere mode when the disgusted heroine calls him sick and depraved, and then becomes determined to kill her, developing a If I Can't Have You... mentality in the process.
In The Not So Short Second Life Of Bree Tanner and its suppliment fic, Ashes through an Hourglass, by Oy Angelina, Bree has a major problem with Alec of the Volturi's infamous Jane-and-Alec following her around until he finally abducts her.
Lullaby from Ultimate Sleepwalker has a crush on Rick, something he's less than thrilled about (doesn't help that she's underage). She won't take no for an answer and repeatedly tries to brainwash him into being her boyfriend.