Doki from There she is!! starts as a fairly minor example of this: She does chase Nabi around the city and can't take "No" for an answer, but otherwise doesn't seem to be all that crazy or violent. Her love craziness reaches its apex midway to Step 3, until she becomes saner, but only after Nabi agrees to become her boyfriend.
While it could be seen this way, keep in mind, "There She Is" is all about showing Nabi and Doki's relationship in a condensed form. It can also be interpreted that Doki's trying to chain away Nabi's social qualms with their relationship, as can be seen in the later steps.
The character of Rift from New Vindicators seems like your usual young teacher/superhero until her obsession with Michuru comes out. Then people start dying.
A gay example in Miller from the third volume of Yotam Perel's Nameless series, who falls for Chocolate Man.
Split-minded Vasto Lorde En from a certain RP game is this way towards the protagonist. "hOW dO YOu do iT? stay so RIGHT wiTh So mAnY. so BeAutiFul."
Shadow Unit: Betty Johnson, the gamma of "Always Crashing in the Same Car". The crazy seems to have started because while she was pregnant, she walked in on her husband raping and killing a woman and subsequently miscarried. The first manifestation of her gamma powers was mind-controlling her husband into killing himself; every year since, she finds a man with the same name and mind-controls him into believing he's her husband. Then she commands him to kill himself on the anniversary of her first husband's death. Most of the episode is from her perspective, through letters she wrote to Reyes; she not only seems to believe that all the Tom Johnsons she married were actually the same man, but she insists to the end, even after being arrested and sent to Idlewood, that "our love is forever".
Cracked noted in this article that the behavior of a woman who might follow Cosmo's suggestions on intimate relationships could very well end up acting like this. The suggestions are downright possessive, obsessive, and overall psychotic. Everything from feeding a boyfriend laxative to crushing his testicles... all over perceived and potentially groundless possibilities of infidelity. At no point did any of the suggestions involve leaving the boyfriend; it was all about punishing them.
In SOTF-TV, Zachariah Johnston is quickly starting to look like a male example. He started out as an Adorkable kid with autism who happened to have a crush on Mae St. Clair. However, he has expressed jealously towards Shawn Morrison (the other part of the Love Triangle), and has flat out attacked other characters who he thinks will hurt her or steal her away, most notably Harold Smythe.