The Joker feels this way about Batman, according to Frank Miller. All of his crimes are part of his "game" to get the attention of The Dark Knight, who he calls "my sweet".
In Death of the Family Catwoman calls him out on it. At least in Scott Snyder's part of the storyline, she doesn't even really have to. Not only does the Joker refer to Batman with romantic epithets, and not only is Batman unnerved when he sees affection in the Joker's otherwise emotionless eyes, but the Joker's campaign against the Bat-family has 'definite' romantic overtones, such as forcing men in Batman and Joker outfits coupled together to dance for days.
Bruce's childhood friend turned villain Thomas Elliot who became Hush. He seems to obsessively stalk Bruce and got plastic surgery to look like Bruce.
Two-Face gets a sort of sick obsession with Renee Montoya after their experience in Batman: No Man's Land. When he learns that she's actually gay in Gotham Central, he just makes it another part of his plan to destroy her life so she has nothing left but him.
Post-Flashpoint, Mr. Freeze is reimagined as one of these. Victor Fries was hired by Wayne Industries to study a woman named Nora Fields who was one of the first people to ever be cryogenically frozen. Victor developed a twisted interest in her, deluding himself into thinking they were husband and wife. Bruce Wayne eventually shut down the project because he was becoming increasingly disturbed by Victor's unprofessional interest in Nora. Victor performed his own private illegal experiments anyway. When Bruce confronted him again, Victor lashed out causing the accident that turned him into Mr. Freeze. When Batman and Freeze face off in the present, Batman calls out Freeze on his delusional "love" for a woman he doesn't even know who is technically old enough to be his grandmother.
Abraham Pointe in Brightest Day was obsessed with a casino waitress named Lisa and stalked her afar with a camera for two years, mistaking it for love. This could have ended very badly for Lisa. Fortunately (well, sort of), the Predator, the Entity of Love, mistook Abraham's insane crush for love as well and possessed him, which got the Star Sapphires and the Green Lanterns involved. Eventually Carol Ferris called out Abraham on his stalker behavior and said to his face that he never really loved Lisa — he didn't know anything about her except for her first name. Abraham had a Heel Realization after understanding that he didn't really love Lisa, which gave Carol an opportunity to separate him from the Predator. You know a (non-existent) romance is messed up when an Eldritch Abomination getting involved turns out to be a good thing.
In Convergence, Flashpoint Aquaman is hunting after the pre-Flashpoint Mera to replace his Mera, who was beheaded by the Flashpoint Wonder Woman.
Cupid aka Carrie Hartnell for Green Arrow. While not the sanest person in general (she killed her hairdresser after getting a perfect haircut so no-one else could ever have hair that good), she takes the crazy to new heights thanks to her obsession with Ollie. In an effort to win his love, she has been killing off the members of his Rogues Gallery. She's done pretty well too; she even killed the superpowered crime boss Brick with a wrecking ball. She also tried to get Ollie to kill his Evil Counterpart Merlyn, thinking that this would make him love her. When that failed due to Ollie following Thou Shalt Not Kill, she chained him to subway tracks and planned to die with him. While Green Arrow and Black Canary were able to get out of this situation in one piece (Merlyn wasn't so lucky — Cupid slit his throat as a distraction), Cupid hasn't given up yet.
In Robin Tim attracts the attention of Mafia Princess Darla Aquista who eventually forced a kiss on him at school. After her death and resurrection she used her new abilities to destroy cars and threaten old classmates to find out Tim's new address then showed up on his doorstep and tried to talk him into helping her kill Robin (not knowing that Tim is Robin) in order for them to start their "new life together" even though he repeatedly states he has no interest in her. She doesn't even think committing homicide in front of him will get in the way of her plans since she "know[s he'] upset but [he]'ll forgive [her] in time". Tim has to call in super-powered help to deal with her.
Oh but Tim's lucky in comparison to Dick Grayson aka Nightwing who attracted the attention of Tarantula an Anti-Hero who became obsessed with him to point where she manipulated an encounter with Nightwing in such a manner that Barbara Gordon, his girlfriend at the time, broke up with him. Even getting arrested didn't keep Tarantula away from Dick as she broke out of jail and continuously got involved with his crime-fighting pressuring him to break the no-killing code and when he poisoned and left immobile on a roof top Tarantula took the advantage by taking his pants off, sitting on his crotch and infamously raped him. It's especially jarring as prior to this Dick Grayson being a ridiculous Chick Magnet was Played for Laughs, but this event made Dick feel disgusted and ashamed.
In Nightwing (Rebirth), Raptor is this for Dick's mother, Mary. She stole medicine to cure his leprosy and he fell head-over-heels for her. It's implied they had a relationship at one time but she broke it off. Her murder hit Raptor hard and it shaped his persona. He then took up stalking Dick to "protect" him and carry out the "justice" he feels Mary would have wanted.
Superman has been stalked by various women, including Maxima, The Queen Of Fables, and Obsession.
Heck, Lois Lane herself was often portrayed as this, intentionally or not, during the Golden Age and Silver Age (and even a little bit into the Bronze Age). Modern writers have struggled ever since to push her away from that.
Pre-Crisis Lana Lang was often portrayed as this, too. She was infatuated with Clark Kent/Superboy since they were teenagers, and she never stopped. Post-Crisis writers portrayed her as someone who had a crush on Clark long ago but got over it and is okay with being his friend.
Supergirl: Powerboy became obsessed with Kara in Supergirl: Identity after catching a glimpse of her as a Female Fury. He created a shrine and became a superhero to impress and seduce her. However, he grew more and more possessive, and beat the crap out of her when she tried to visit Captain Boomerang (Owen Mercer) in the hospital. Supergirl defeated him in spectacular fashion.
Teen Titans. The second Clock King is obsessed with Rose Wilson aka Ravager. He murders his lover, The Disrupter, for trying to kill her.
Wonder Woman (1987): While Artemis was the current Wonder Woman due to the events of The Contest and Diana was working with PI Micah Rains she responded to a client who was worried her stalker was going to kill her or her fiancé, and who had already killed her pets. When Diana arrived to talk to the client the stalker was hiding out nearby in some bushes and tried to argue with Diana that he loved his victim which Diana refuted.
Lampshaded and spoofed in one of the early issue's of first ongoing series, when he's looking over his not-entirely-unrequited crush Siryn (paraphrased):
Deadpool: Once upon a time, watching over a girl in her sleep used to be romantic. Nowadays it's called "stalking" and generally considered "Trespass".
Sort-of subverted later, when Siryn tells Deadpool she knew about it all along and actually appreciates it.
When Deadpool was institutionalized he unbelievably started making real progress towards sanity. Too bad his therapist Dr. Ellen Whitby was a loony stalker even crazier than him. And by crazy, I mean keeping his lost body parts (which he regenerates) in her fridge crazy.
Kathy Dare. She stalks him and later shoots him when he rejects her. At her trial she plays the victim and claims that Tony abused and stalked her (which, unfortunately, is also a tactic of some real-life stalkers).
At one point, a sentient Iron Man armor takes on all the attitude of an abusive boyfriend, cutting off Tony's access to the Avengers, pissing off then-girlfriend Rumiko into leaving, breaking Tony's arm when he resorts to using an older set of armor in an escape attempt, and finally taking him to a deserted island and tying him up while it spends a week attempting to convince him that they're "perfect for each other".
Marvel's The Mighty Thor is no stranger to this either. He's been stalked at various times by Amora the Enchantress, her younger sister Lorelei, his niece Hela, and his former teammate Moondragon. Magic, mind control rape, and blackmail, oh my.
Mystique toward Iceman in "Kill Or Cure". After throwing him out of his Blackbird, trying to poison him in hospital where he was recovering, and then causing a truck that he was hitching to crash, she stood on top of one of the Pylons on San Francisco's Bay Bridge with a bomb. When Iceman went up to try to talk her down, she begged him to join her in a suicide pact; instead he laughed at her and called her a loser. She did not take it well; "You'll see me one more time; I won't be wearing this face or body, but you WILL love me!" and threw herself off.
Paper Doll, although her crush was on celebrity Bobby Carr who is not exactly one of the main Spider-Man cast. Her stalker tendencies were elevated to the point where she lashed out and attempted to murder everyone who dared to try and ruin Carr's name, including a woman selling her negative story about him to the news and tabloid reporters. Made all the more dangerous when combined with her ability to become paper-thin, blend in with any surrounding, "compress" the bodies of those she envelops and leave them as thin as herself (unable to stop themselves from suffocating in the process) and administer lethal papercuts strong enough to slice through Spidey's webbing.
Mary-Jane Watson- being an actress/supermodel has had several, starting with Jonathan Caesar, an It's All About Me type who kidnapped her in the sincere conviction that because he wanted to marry her, little things like her not agreeing or already being married shouldn't stand in the way.
Felicia Hardy alias Black Cat started out being one of these towards Spider-Man. She even had a room sized shrine dedicated to him, which he found a bit unnerving (but not enough to stop him from dating her for a while).
Speedball: I just wanted to say thanks for everything you did! Also for all those nice letters you send. Squirrel Girl: Oh... You—You know about them? Speedball: I read all my fan mail! That plus my manager alerted the FBI about them.
This is Thanos' relationship with Death — she's his one true love, and he longs to die so he can be with her, but being as he is a comic book character, getting that to stick is... difficult. There are occasions where she does proclaim to have feelings for him, or at least something similar. The problem is that Thanos is Thanos, and she's put off by it. And his constant grabs for god-like power, by her words, put him beyond her power. Death apparently doesn't do long-distance relationships.
When he died during Annihilation, they apparently had a thing going, and were happy. Then he got brought back to life, and was made unable to die.
There is a hilarious moment where Death from Neil Gaimans The Sand Man makes a cameo in X-Men but says she needs to go before that creep Thanos show ups looking for her.
David "Whirlwind" Cannon in the original canon, who became obsessed with her while posing as her chauffeur for what was originally just a theft plot, then expanded to include trying to kidnap her as well. Recent storylines indicate that he's not over this obsession, even after she's dead.
Arthur "Living Laser" Parks (also from the original universe) fell for her at first sight after originally stalking a friend of hers and attempted to win her by kidnapping her and trying to kill the rest of the Avengers. He was still hung up on her as of a cameo in Avengers #300, though it hasn't been part of any plot since then.
Erik Josten stalked her in, of all places, the Marvel Adventures-verse, where he was an employee of her father's who tried to make it look like her friend/crush Hank Pym had up and disappeared in order to get close to her.
Kimura's pursuit of X-23 veers way past her role as X's handler and into this territory. She's positively obsessed with Laura, to the point of threatening to track down and kill her aunt and cousin out of spite for escaping, and much of her behavior makes her come across as a jilted ex, to the point that it's lead to a lot of Foe Yay shipping by fans.
The Morlock Caliban was this towards Kitty Pryde during the 80s. In fact, one incident lead to the legendary fight between Storm and Callisto. There was one incident where he had an infatuation towards Jubilee, but that ended quickly when Sabretooth got his claws on him.
Briar Raleigh for Magneto. She falls for him after he crushes her leg with her car, without even noticing her, and starts studying up on and then following him.
Used as part of the backstory in the first Blacksad comic. When Blacksad meets her Natalia is harassed by a stalker, and hires Blacksad to get rid of him. Blacksad does so by shoving a gun in the guy's mouth and threatening to kill him.
In PreTeena, Johnson Pinecone teeters on the verge of this in his pursuit of Jeri Keene, always managing to be there and knowing from observation what she likes.
Darth Vader, of all people, got one of these during the Star Wars "Vader: Dark Visions" comics, an Imperial nurse who developed a decidedly one-sided attraction to the Dark Lord of the Sith, keeping souvenirs of his cybernetic surgeries and even developing delusional fantasies of Vader being her protector. But when she finally sought Vader out in his chamber to try to make something of this, she promptly got Vader's saber through her chest for her trouble.