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.
Arcturus Black is one to Harry in If Thems The Rules, staking out Diagon Alley for weeks for a chance to talk to him.
In Do Not Meddle in the Affairs of Wizards Ginny had a severely-allergic Luna stung by a bee just because Harry smiled at her and kissed her on the cheek as thanks for giving him a present from Hagrid.
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.
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
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.
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.
Luminosity has this between Demetri and Allirea. The former is a vampire, which means mate bonds are supposed to be automatically mutual. He never quite gets that they aren't, so he sees her trying to get away as a game.
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.