Anya and Dimitri in Anastasia. Mentioned by Vlad who calls it an unspoken attraction.
The centipede and the spider from James and the Giant Peach are constantly fighting and teasing each other in the beginning of the film but end up in love with each other. At one point the spider says that she doesn't know if she wants to kill or kiss the centipede.
Alas, they mellowed out in the end of the first movie
Friendly rival, yet pompous Grayson may be handsome like Surly, but he ended up much worse
Tiana and Naveen from The Princess and the Frog, although the sexual tension only surfaces when the belligerence starts to die down.
Blu and Jewel from Rio. Though Blu is definitely not a jerk, Jewel's initial judging of his inability to fly and him being a pet does tend to rub him the wrong way. They actually do end up together at the end, though, even having chicks as well.
Jake: Honestly, I'm tryin' to be a gentleman about this. Now just, get down on your knees, stick your ass up in the air, and don't move 'til I tell ya.
Alfred Kralic and Clara Novak in The Shop Around the Corner. To make matters worse, each has got a wonderful pen pal with whom they're falling passionately in love...
A classic example from the film The Mad Miss Manton, there's Melsa Manton and Peter Ames who hate each other at first, but they eventually get used to each other.
Tori and Junior in Roll Bounce, from the second they meet. They have The Big Damn Kiss right after X and Naomi do to the surprise of only Tori's mother. For that matter, given the argument they have on first meeting, Vivian and Curtis certainly seem on track for a relationship by movie's end.
Upstream Color has a very unusual example. Jeff and Kris have both unknowingly come under the influence of a parasite that causes their minds to be linked with others. They're subconsciously drawn to each other due to the lingering effects of the parasite, but their first few scenes together are awkward, tense and irritable. They have no reason to be with each other except for reasons that are beyond their understanding.
It's implied that this was the backstory for the protagonist's first serious relationship in the Adam Sandler's Big Daddy. We first see Sonny and Vanessa at the beginning of the movie, during (what is presumably) their third-to-last encounter, and their very last encounter on at least superficially friendly terms. They can't stop arguing, with Vanessa telling Sonny he's lazy and childish and Sonny (a bit more charitably) telling Vanessa she's uptight. Vanessa finally storms out of the apartment, and it becomes clear that Sonny might never see her again. But the funny thing is, he actually falls into depression about this for a time, and ponders how to win her back. We also hear him discussing Vanessa with other characters, his best friend at one point saying that she "worshipped" him ten years ago when they were at college, and at another point Sonny himself remembering that she used to go to the sports bar with him and tease him by rooting for whichever team was playing against the one he liked. So there was something there for all those years, but we just arrived too late to see it.
In Singin' in the Rain, Don Lockwood's relationship with Kathy Selden is quite belligerent, but quickly develops into sincere attraction. Subverted by Don's behavior toward Lina Lamont—Lina fancies herself in this kind of relationship with Don, but he genuinely dislikes her, and his efforts to reject her only fuel her delusions of romance.
The relationship between Pearl and Lewt in Duel in the Sun (1946). It ends tragically with them killing each other.
In Once Upon a Spy, Jack Chenault and Paige Tannehill spend the first 2/3rds of the movie alternating between sniping at each other and flirting. Things start to defrost after an Intimate Healing moment.