One of them is bound to the other and hates it. The hostility is about who holds the rope.
The grudge: a necklace and the word "sit"
3. Inuyasha
Feudal Japan · action fantasy
Kagome falls down a well into the past, pulls an arrow out of a half-demon who's been pinned to a tree for fifty years, and he immediately tries to take the jewel she's carrying. So the village priestess puts a necklace of subjugation on him, and Kagome learns that if she says "sit," he hits the dirt face first. For a very long stretch of the show the romance is nothing except that leash: a boy who could kill her and a girl who can floor him with a word, both pretending the arrangement is purely practical. The Kikyo triangle makes it hurt more than the premise suggests.
Does the anime finish it? Yes, eventually. The original series stops mid-story, but The Final Act adapts the manga through to the end, marriage included.
The grudge: a human for a master
4. Kamisama Kiss
A shrine in the suburbs · yokai romance
Nanami, freshly homeless, is kissed on the forehead by a stranger and inherits his shrine, his job as a land god, and Tomoe, the fox familiar who has served that shrine for centuries and is disgusted to find a teenage girl now outranks him. He is openly contemptuous. She is stubborn and broke. Then she binds him as her familiar with a kiss, which the show treats as both a legal instrument and the most embarrassing thing that has ever happened to either of them. The romance grows out of the paperwork, and Tomoe's slide from "I will not serve a human" to quiet devotion is the best-drawn thaw on this list.
Does the anime finish it? No. Two seasons and OVAs, then it stops. The manga does finish, and finishes happily.