While fans have enjoyed going into the various alternate pairing ideas for The Breakfast Club, Bender/Allison is clearly the most popular. Due to how both Bender and Allison are quite the outcasts, Bender/Allison fanfics have a known tendency to give them a Birds of a Feather dynamic. Though to be fair Bender's line to Allison early in the movie "I've seen you before you know" has been occasionally used as Fanfic Fuel.
Fans of the Brit Com film Four Weddings And A Funeral often complain that the main character's witty, lovelorn friend Fiona is a far better match for him than the vacuous American he ends up with.
In Pretty In Pink, Duckie/Andie was originally supposed to be canon but test audiences didn't like it, so the ending was changed.
In the DVD commentary for Starship Troopers, director Paul Verhoeven says fans wanted Carmen to die and Johnny to end up with Dizzy, proving that it isn't only fans who have preferred couples. Considering that in the original book Dizzy is male and Johnny and Carmen have at most a one-night stand together, this wouldn't have been such a bad change compared to most of the rest of the changes Verhoeven actually did make.
Raoul and Christine end up together in Phantom of the Opera, but most fans prefer Christine to be with Erik - especially the ones that go by the 2004 version of it (where the Phantom is portrayed by Gerard Butler). Also see the series' entry in the Theater section.
A lot of fans of A Knight's Tale aren't fond of William/Jocelyn, instead preferring to hook him up with his hard-working friend Kate. Chaucer and Wat are also a major Fan Preferred Couple.
Jareth/Sarah from Labyrinth is quite popular, in spite of Sarah flat-out rejecting Jareth's offer to make all her dreams come true at the end of the film. It probably has a lot to do with Jareth being played by David Bowie.
In the Inception fandom, Arthur/Eames and Arthur/Ariadne is this. It's the version where the fandom has no Official Couple, though; the only canon couple involves entirely different characters.
The Dom/Ariadne pairing also has its fair share of shippers.
Fun fact: on ff.net, there are virtually no pairings for Sebastian/Annette from Cruel Intentions. Pretty much everyone was rooting for the bitchy, scheming Kathryn.
In Red Eye, many ship Lisa and Rippner, in spite of (or because of?) all the attempted murder on both sides, as well as the intense chemistry between Rachel McAdams and Cillian Murphy, especially during the lavatory scene.
In Push: Compare Nick and Cassie's number of YouTube videos (over twenty) to Nick and Kira's (none). Yeah.
The Official Couple in the Star Trek2009 movie is Spock/Uhura. There is a sizable section of the fandom for whom Kirk/Spock is the Fan Preferred Couple, some of whom believe that the former relationship was put in purely to dissuade Kirk/Spock shippers. (Though the movie has also spawned a sizeable Kirk/McCoy following.)
Fans of the Rupert Grint movie Cherrybomb can generally be split into two categories: devoted Malachy/Luke shippers who simply ignore Michelle's existence; and batshit crazy, foaming-at-the-mouth Malachy/Luke shippers who openly detest Michelle and loudly wish her dead. This is a pretty extreme reaction given that in canon, both guys are seemingly straight and spend most of the movie competing for Michelle's affections. That said, several cast members have alluded to the strong homoerotic subtext of Malachy and Luke's relationship, so it probably doesn't exist entirely in the minds of yaoi fangirls.
For X-Men: First Class, Erik/Charles is the official pairing, even according to certain screenwriters and actors. It's incorporated even in fics that involve the younger X-Men (by having them act as parents), and those who do ship Erik/Raven or Charles/Moira are a small minority.
In the Original trilogy Logan/Rogue is more popular than Logan/Jean and Bobby/Rogue.
When it comes to The Avengers, slash pairings like Thor/Loki, Steve/Tony, Bruce/Tony (or the combined Steve/Bruce/Tony) tend to be more popular than those characters with their het love interests such as Jane, Pepper, Peggy, and Betty, mostly due to the fact that those characters are nearly/completely absent from the film (or, in Peggy's case, old/dead).
However, this only applied to The Avengers, and not to the Marvel Cinematic Universe movies that those characters originated in. But in the case of Captain America, Steve/Bucky tends to heavily rival, if not eclipse, Steve/Peggy in many fan circle.
Loki/Black Widow often gets this treatment thanks to a healthy dose of Foe Yay they recieved in the film when they're not slashing Loki with the male members of The Avengers. It's enough to rival, even eclipse, fans of Hawkeye/Black Widow.
A chunk of the Now Voyager audience seem to prefer Dr Jaquith as a romantic partner for Charlotte, finding Jerry a little dull in comparison to the charming Jaquith. Bette Davis herself said that she imagined Charlotte marrying Dr Jaquith after the film ended, as Jerry was 'too weak' for Charlotte.
Schindler's List has Amon and Helen, pairing occasionally supported by viewers, despite unlikelihood of it ever possibly working out, particularly since Amon mostly seems to see her as something he likes to possess than actually caring about her.
Rahul and Nisha from Dil To Pagal Hai have a following, if only because Pooja is sometimes considered TOO perfect...
The Foe Yay between Daniel Plainview and Eli Sunday in There Will Be Blood is so prominent that nearly all of the fanfic written is for this ship.
Some The Great Race fans consider Maggie/Professor Fate as having more chemistry than Leslie/Maggie. Probably not helped by how one hilarious scene has her actually kissing the guy. There's actually some Reality Subtext here. Natalie Wood was forced by the studio to do this movie against her wishes, then to make matters worse she was paired up with Tony Curtis. They'd already done two films together and had developed a passionate hatred for each other, so the lack of chemistry between Maggie and Leslie was genuine.
While Mo is paired up with Scott in Lemonade Mouth, fans like to ship her with Charlie instead. Meanwhile, Stella doesn't end up with anyone, but it hasn't stopped fans from pairing her with Ray, probably due to all the Foe Yay.