Cia of Hyrule Warriors was once a guardian of the timeline who was twisted by her obsession with Link and her jealousy of Zelda. Her Temple of Souls is essentially a massive Stalker Shrine covered with statues and portraits of various incarnations of Link.
Xenosaga Episode III: Kevin the Red Testament stalks Shion everywhere she goes, almost justified by the fact that they had an intimate relationship when he was alive. When Shion dumps him, he doesn't take it too well though, he attacks all of them. Someone just can't handle rejection too well.
Also, Clara, who is compassionate and helpful, even as she mercilessly stalks Gilder. It came to a full-on airship battle between their two ships... Though it's also implied Gilder enjoys being chased, even if he denies it, and the two seem to get along well enough when the plot brings them together to both work with the heros.
And then there's Valkyrie Profile 2 Silmeria, in which he actually goes back in time, abducts her sister Silmeria Valkyrie, uses her power to defeat Odin so that he can absorb his power and steal Gungnir, and creates a twisted new realm. Why? To lure Lenneth to come and stop him, so that he can become one with her. Literally.
Played with in Metal Gear Solid 3 with Ocelot's fervor to find Snake. At one point, an optional conversation reveals that he ate all of Snake's food while Snake was imprisoned because he thought eating the same foods would make them similar. It doesn't help a lot that the other (female) "love interest" thinks the stalkerish crush is cute and won't stop teasing Snake about it. He's too oblivious to have a clue what she's on about. (In his defense, it is The '60s.)
Also in the first Metal Gear Solid, it's reported that Sniper Wolf tends to end UP as a Stalker with a Crush because of how single-mindedly she becomes obsessed with her targets, with a hint that she was starting to go this way with Snake.
And Naomi from the same game. "You were all I thought about for two long years. Like some kind of twisted obsession." (One of the retranslations of this line, available on the Metal Gear Solid 2 disc, even changes the last sentence to "It was like being in love".) Her feelings towards him change over the course of the game, but in The Twin Snakes, she breathes in his scent, has great trouble taking her eyes off his nearly-naked body, and sits closer to him than he's comfortable with, causing him to shuffle away as she edges closer, and even attempts to grab his bottom at one point - all during the Briefing, when she's just injected him with the virus which she specifically designed to kill him. Towards the end of the game, she makes an unauthorised transmission to tell Snake 'something', but is booted off the frequency before she can say it - but Word of God says that it was a declaration of love.
Near the end of Knights of the Old Republic II, if you're playing a female character, Darth Sion will confess to having developed an obsession with you. His reason for wanting to kill the Exile is because he can't risk being Distracted by the Sexy, as this would cause him to lose focus on The Power of Hate, which is all that's keeping him alive.
Similarly, on the Peragus level, some of HK-50's lines have a decidedly more possessive quality when the Exile is female, particularly his righteous anger at Coorta's interference. To hear him tell it, his massacre of the colony is motivated as much by a sick sense of chivalry as it is by his desire to collect the bounty on her head and general psychopathy.
Visas Marr, a Sith apprentice initially sent by Darth Nihilus to kill the Exile, confesses to a male Exile that she loved him the moment she felt him through the Force. As he's the only person to have experienced death and destruction similar to what she felt when her master destroyed her homeworld. She has a creepily slavish devotion to the Exile and would happily end her own life if they asked.
HK-47 considers love to be "...knowing your target, putting them in your targeting reticule, and together, achieving a singular purpose against statistically long odds."
This is at the highest extreme for being an insane stalker in Sonic Battle, where Rouge (the current player character) faces Amy in a fight. When Rouge wins, Amy actually hallucinates that Sonic is by her side and you have to fight them "both".
LeChuck in the Monkey Island games. His obsession with Elaine Marley not only brings him back from the dead but incites some truly wall-banging logic, as in The Curse of Monkey Island when he decides to attack Plunder Island in hopes of winning her heart. "Now with the demon flames of this voodoo cannonball, I'll blast my significant other into the significant otherworld, ha ha! That'll show how much I truly care."
While we're on the subject, Marta is a heroic example. And it's played for laughs. To be fair, she eventually does realize how shallow she's been about it. Her moving away from that is when the romantic arc between her and Emil can actually happen.
In Tales of Vesperia, Zagi borderlines on this with his violent obsession with the main protagonist Yuri Lowell.
Zagi: "Oh I'm soooo happy to see you again!"
Yuri: "Dammit, how long are you going to keep chasing us?"
Zagi: "I guess you're just as happy we met as I am!"
The song "Destiny" from DDRMAX2: Dance Dance Revolution 7th Mix has the female singer singing, "I'll keep on following you, wherever you go / Following you for the rest of my life."
Stanley Coleman towards Heather in Silent Hill 3; he leaves letters with dolls for her, and the poem you need to read to solve a certain keypad puzzle was supposedly penned by him. Nevermind that he's supposed to be dead and that his corpse is one of several stashed in the hospital crematorium, if you believe that one phone call. Claudia may also count as well.
The creepiness factor of this is played to the hilt in F.E.A.R. 2: Project Origin: Alma is hunting Becket because she wants to have a child with him. Whether he wants it or not.
Also, Alma is apparently very much in love with Becket.
Persona 2 features a very creepy stalker of Ellen/Eriko Kirishima, covered with bandages and wielding a chainsaw who wants to express his love of her by killing her. This later becomes a pivotal point that the stalker professes that Ellen/Eriko is Not So Different than him. Indeed, judging from her interactions with the protagonist of Persona, Ellen/Eriko has a massive crush on him and her worst fear is to be treated like a Stalker with a Crush by him, the same way she treats this stalker.
Aigis. She has a reason but sneaking into a person's room crosses the line! She even keeps records of how long it takes her to pick the door lock every night.
Aigis starts off as a Stalker Without A Crush, only following the protagonist because she sealed a piece of Death inside him 10 years ago and wanted to monitor it, although she doesn't remember. She eventually develops genuine feelings for him.
Additionally, throughout the course of the school year you can bear witness to the saga of a pair of schoolmates at Gekkoukan High. At first, it's a girl silently stalking some random NPC from afar —hiding behind a tree, standing just around the corner, sighing at him from the shadows— while he has the distinct feeling that someone is watching him, and eventually he confesses he knows she's there, but still doesn't acknowledge her. As the year goes by, the tables turn: she learns of his less pleasant habits and personality traits, while he's grown so used to having her around he starts stalking her, and she's creeped out by this. Come graduation, they realize how much time they wasted on this, but the girl is still back to stalking him.
Mitsuru also has a particularly obsessive secret Fangirl who grows increasingly (but hilariously) excessive in her affections, to the point she wants Mitsuru to run her over with her Cool Bike, and considers "bumping off" someone from the Student Council so she could take their place and thus be closer to Mitsuru, its current president.
Elanee in Neverwinter Nights 2, though it's never actually explained why she's been stalking the protagonist since he/she was a kid (and raising Fridge Logic issues if the protagonist is an elf or similarly long-lived race, since Elanee seems to be around the same age as the protagonist in maturity). With female protagonists, the "With A Crush" part of the trope is dropped... though a mod exists to change that.
Hypothetically, given the progression of maturity for elves in Faerun, she might have been given an assignment as early as 40 or 50 (approximately equivalent to 11-12 for a human), so her having tracked an elf protagonist since childhood might not be so far-fetched. The fact that she spent likely around 60 years in this case following an elf her own age around, while going through puberty and not having any people near her own age in the Circle, and never attempted to contact him, is either a testament to her enormous willpower or the fact that all of the Neverwinter Nights games were actually written assuming a good male human.
Regarding the fridge logic of elves' maturity, it's worth noting that in Faerun elves reach physical maturity around age 20, but aren't considered to reach mental/emotional maturity until around 120. This is mostly cultural, as elves are so long-lived (about 700 or so) that they feel one of their kind is little more than a child until they've had at least a century of life experience under their belt. Furthermore, the Attack on West Harbor happened when the PC was still a baby and within living memory of the rest of the human village (with the PC's human childhood friend Amie losing her parents to the attack when she was a baby), so the PC by default can't be more than 20 at the game's start. So, it makes sense for the century-year-old Elanee to have watched the PC since infancy. As for an Elven PC (or other similarly long-lived race), one could probably chalk it up to them being physically 18-20 at the game's start, and simply being Younger Than They Look if their race doesn't typically mature that fast compared to humans.
There are some details as to why given in the game, and more is somewhat revealed in content that didn't make the final cut of the game due to time constraints (but traces of it exist and can be found with the toolset). The Circle of the Mere didn't trust the PCs foster father Daeghun and was convinced he possessed all sorts of dark secrets (related to why the Mere was dying) that they wanted to know. Elanee's final test as a member of the Circle was supposed to be to live among the people of West Harbor for a time and keep watch over the PC, but some of the Elders didn't think that was a good idea and decided not to let her. Elanee would still watch over the PC anyway (leaving her duties for several months at a time to do so), but always did it from the shadows. When the Githyanki attacked West Harbor the Circle of the Mere ordered her not to help the villagers (hoping the attack would force Daeghun to reveal some of those secrets...) and she cried for the first time in over a century.
Valter, Valter, Valter. The psychopath is rather fixated on both Ephraim and his sister Eirika, but while he simply wants to kill Ephraim For the Evulz, he has other plans for Eirika, as his rather transparently sexual lines to and about her demonstrate...
Valter: Mmm... I've been waiting for you, Eirika! Eirika: Who are you? Valter: Have you forgotten? We met once at Castle Renais. No? Look closely, Eirika. Do you not remember the face of he who will master you? Eirika: Wha—!? Valter: Yes, resist. It's much more fun for me that way. Come, Eirika. I should like to tame you.
From the same game for contrast, there's a more comedic version of Lute the mage towards Artur the monk as one of her hobbies is "monk-watching."
In Fire Emblem: Path Of Radiance, Aimee, one of many women in the game attracted to Ike, is this to him (after he takes down an easy target, she starts swooning over him, and later in the game he is willing to interrupt Soren's work in order to hide in his room from her). This continues in Radiant Dawn, even going as far as forcing him to call her beautiful so that she can tell everyone that he likes her back. Luckily, most of the time, Soren is able to rescue him.
In Fire Emblem Awakening, Tharja the Plegian dark mage becomes instantly enamored with your Player Character the moment she joins your army, obsessively following you around everywhere, and even bringing your name up in her support conversations with other characters. You're free to return her feelings by marrying her if you wish if you play a Male Avatar.
In Fire Emblem Fates Rhajat becomes obsessed with your Player Character after the Avatar saves her from a Faceless. It's strongly implied that Rhajat and the Avatar are either reincarnations or preincarnations of Tharja and Awakening's Avatar. Again, you're free to return her feelings and marry her, this time as eithergender. Note, however, Rhajat's obsession with the Avatar doesn't exist if the Female Avatar is Rhajat's mother instead.
And in Fire Emblem: New Mystery of the Emblem, there's Mallisia towards The HeroMarth, who has over the top princess fantasies about marrying him (even after finding out he's engaged), distorting their first meeting in her mind so that she believes that he fell in love at first sight with her, constantly Squees thinking about him, and is stated by Kris to have snuck into his room several times. Though thankfully she gets over this easily after Kris convinces her otherwise... Only to latch onto him if he's male.
BlazBlue's Bang Shishigami is this towards Litchi Faye-Ling, combined with Dogged Nice Guy, albeit it's quite a one-sided love affair, and she's rejected his advances down numerous times. Although he secretly lusts her, he is tempered by his morals as a ninja in service of justice. She's eventually spotted and confronted him over this, but over the course the story, he's respectful and understanding of her, even developing a friendship with her through it all (even if he still proclaims his love for her every now and then).
Haunting Ground. Good god, Riccardo. The creep is well known for being Fiona's incredibly persistent stalker. Shall we list all of his offences? He causes Fiona's parents to get into a deadly car crash, kidnaps the unconscious Fiona and strips her so that she has to go around the mansion naked, carves a wooden statue of Fiona pregnant (and tells her that he's going to make her that way), constantly tells her "You are mine, Fiona," stripping her again and giving her an ovulation test while she's unconscious to determine when he can impregnate her), drugging her and molesting her, out-and-out stalking her with a gun, and... if he catches and kills her during gameplay, the Game Over has him raping her body. "Fiona, let me into your womb!" Aieee.
Come to think of it, Lorenzo is one towards her, as well. The guy actually watched her get naked and change her clothes through a secret eyehole in a painting on the wall. All of this is so much worse when you find out he's her insanely old grandfather. Fiona really has one happy family, doesn't she?
Played around with in Mass Effect 2; many of the earlier advertisements for the game made Legion appear to be obsessively searching for Shepard, ostensibly to kill the Commander. It turns out that he was looking for Shepard so that he could join him/her, and once Legion is actually recruited, it quickly becomes apparent that he's not only sane, but one of the most level-headed members of your team. He does, however, have a bit of a crush on Shepard—when questioned about why he used Shepard's wrecked armor to repair himself when there were plenty of other, more suitable materials nearby, he hastily dodges the question.
Legion: There was a hole...
His answer speaks volumes when Shepard asks him why his/her armor, why wait two years to fix himself:
Irwin the Juggler from Pokémon Gold and Silver. He's a minor NPC, just a trainer you battle at a fairly early point in the game. However if you give him your number in Crystal when you play as a female he's always calling you, more than anyone else, saying how he saw you accomplish so-and-so. In HGSS he's gender neutral.
In Pokémon Black and White, N shows more than a few signs of this towards the player character, as he quickly fixates on you and starts following you around everywhere you go. The clearest example is his behavior in the infamous Ferris Wheel scene, grabbing you and trapping you in an enclosed space to tell you he's the leader of the bad guys, and he's going to overthrow Unova by force, and then you and he are going to be friends, right? This could be explained by him having No Social Skills due to basically being Raised by Pokemon for most of his life, however. Later, in Chargestone Cave, he indicates that he's using his father's ninja allies to keep tabs on everything you do.
Silver (upon meeting you at the Burnt Tower): I HEARD YOU WERE SLEEPING THERE.
Silver (after defeat): I TAKE A FANCY TO THE STRONG WINNER.
Silver (while following you around): YES, OUR LOVE MUST BECOME STRENGTH.
An interesting, rare heroic example in Dragon Age: Origins, if you played a male Warden who romanced Morrigan since the Witch Hunt DLC is about tracking her down after she left you. However, her leaving was due to necessity rather than choice, she still has very strong feelings for you and will happily welcome you back if you choose to stay with her.
In Tales of the Abyss, there are definite elements of this in the way Dist obsessively follows Jade around, although Dist claims it's because he wants to prove he can "surpass" Jade.
The player character from the Biko series as stalking the girls is the objective, then the player can either get the "rape" ending or the "love" ending, with any of the girls.
In Jak II, Erol takes an unhealthy interest in torturing Jak for two years straight and then becomes even more obsessed when he escapes.
Erol: I want more than just to win, eco freak... I want you!
In Saints Row: The Third, the Eastern European Female Boss makes it clear she has a thing for Pierce. At one point she wonders if she can get cameras installed in his room, and send him a sex toy from a "secret admirer." Eventually, she admits to wanting to have sex with him in front of a live studio audience.
In Dishonored, if you want to go the pacifistic route and not kill Lady Boyle, you can instead knock her out and deliver her into the clutches of one of these. Who assures you that she will 'never be seen again', and that she'll have the rest of her life to learn to love him. Eventually. As is the case with some of the other pacifisticoptions in this game, you might wonder if you're really doing her a kindness here...
Herbert the Hermit in Borderlands 2: Captain Scarlett and her Pirate's Booty. He used to be part of Captain Scarlett's crew before she kicked him out for his stalker behavior. He has a part ofCaptain Blade's compass and he won't give it up until the Vault Hunters retrieve several volumes of his (terrible) poetry. When the Hunters finally get that compass piece, they can give Herbert the gift that Scarlett wants him to have. It's a bomb.
Borderlands: The Pre-Sequel! reveals that Professor Nakayama's obsession with Handsome Jack goes beyond simple devotion and straight into creepy infatuation even long before Jack became Handsome Jack. His sidequests generally involve getting the players to help him get Jack's attention or approval, all of which simply ends with Jack screaming at him for his ineptitude (all the while getting his name wrong) or complimenting the Vault Hunters for a job well done. The Jack Doppelganger in particular starts getting really disturbed by him.
The heroine in Save the Prince is one. She keeps having dewy-eyed fantasies about her and the title character being in love "forever and ever" despite the fact that he only knows her as the "strange servant" who stands on the castle balcony and waves to him every morning.
In Final FightRevenge, Poison becomes this for Cody. Thankfully, it avoids using the fact that Poison used to be a man for squick; Cody is against her affections because she's a criminal. Also, Poison ends up getting over Cody by the game's end.
Yandere-chan is too shy to confront Senpai directly, which means that if you want to follow him, you pretty much need to stalk him if you don't want to disturb him. She even has a Stalker Shrine, which has a bandage, a half-eaten apple and a toothbrush she stole from Senpai's home. Note that she is also a Stalker Without A Crush, as unless you want to eliminate someone in the spot, Yandere-chan has to stalk them for the perfect opportunity to get rid of them or spy on them for info she can use.
Ryoba did much of the same as Yandere-chan: she had her own senpai she stalked from afar, and is confirmed to have killed at least one rival who got in the way. Eventually she took matters into her own hands and kidnapped her senpai. She's Yandere-chan's mother and her senpai is Yandere-chan's father. Yandereness runs in the family.
Alpha builds that have the Matchmaking method programmed in have Riku Soma stalking Kokona Haruka, watching her as she is working in the Cooking Club. Yandere-chan can help him hook up with Kokona.