Quite a few fans think Victor Van Dort from Corpse Bride ended up with the wrong woman and Emily was more compatible with him; at any rate, he'd gotten to know her far more than Victoria.
The Secret of NIMH has Justin and Mrs. Brisby. Some fans tend to mistake Justin's chivalry as romantic advances on the widowed female of another species. A rumored storyboard depicting the two of them kissing only escalated matters (but Don Bluth debunked it as a hoax).
In Tinkerbell, Terrence was supposed to be Tink's love interest, but a significant portion of the fandom thought he was a pretty boy caricature, and thought that Tink/Bobble was much more appealing.
Historically, Rolfe does marry Pocahontas, but fans of the Disney version think she belongs with John Smith (a sentiment that even The Walt Disney Company clearly shares anyway, although mostly because they ignore the direct-to-video sequels).
Felidae has Francis/Felicity. Which might have happened in canon had Felicity not been gruesomely beheaded.
Some fans of Paprika have lots of trouble accepting that Chiba loves Tokita, and would rather have had her end up with Konakawa. This ignores how the fake ending with Konakawa and Chiba kissing in the sunset is supposed to be making fun of trite, cliché movie endings, which implies that pairing them together would have made for a really, really bland and predictable ship.
ParaNorman has very questionable one - Norman and Aggie. Some find the Shipping weird because they are related, but it is also justified because of three hundred years of genetic separation. Also, the song Little Ghost in the credits really enforces it.
In Rise Of The Guardians, Jack and Bunnymund is the most popular as seen by the most amount of fan works devoted to them.
But now it's Jack and Toothiana.
The Yaoi Fangirl faction of Road To El Dorado is, unsurprisingly, siding with the Tulio/Miguel pairing. Interestingly enough, so are the producers. They originally wrote them as lover to begin with, which was vetoed by the higher ups. It's made fairly obvious that they were not ready to give up their original idea and just kept some of the scenes in. They also go to great lengths to say how "cute" and "adorable" they think Chel is, which makes it sound very forced. So, not only fan but also producer preferred couple.
Frozen fans love shipping Elsa and Anna, moreso than any other pairing, due in no small amount to the film's subtext. Elsa and Jack Frost is also extremely popular. Before the movie's release, everyone shipped Anna and Hans due to the classic prince-princess formula. This changed when it was revealed Hans was the main antagonist (and it came out of left field WITH NO WARNING OR HINTS). Cue Disney traditionalists exploding in anger over an evil prince while Anna settles for an ice dealer named Kristoff.