Ship Tease/Film

Tim Burton's adaptation of Alice in Wonderland contains surprisingly sweet moments with Alice and the Mad Hatter. It helps that Alice is now 19-ish, and the Hatter is played by Johnny Depp. Turning himself in to buy her more time is obviously quite useful, but that doesn't explain Alice taking extreme care to return his beat-up top hat and personally busting him out of jail.
- Incidentally, the cast members at one of Disney's theme parks like to tease Alice/Hatter as well.
- The Sci Fi Original Movie/Mini Series of Alice gives tease for this pairing for a few days before making it canon.
Harry Potter and the Deathly Hallows - Part 1: How much false hope can you fill the Harmonians with, David Yates? After Ron's gone, Harry dances with Hermione just to cheer her up. One might think that if Ron had not come back in time, they would have ended up together. Ok, Harry would have drowned in the icy water before they'd have made out.
- Deathly Hallows - Part 2 film puts in a couple of brief-but-amazing scenes to tease the Neville/Luna shippers. "Have you seen Luna? I'm mad about her! About time I told her, since we're both probably going to be dead by dawn." FANGASM.
- Harry/Luna is teased a little bit in Order of the Phoenix with an oddly romantic hand-holding shot near the end.
The Pirates of the Caribbean films were frequently teasing with Jack/Elizabeth, especially their kiss near the end of the second film.
Inception had Arthur tricking Ariadne into kissing him.
Kung Fu Panda with Po and Tigress. It is said in the commentary for the first movie that Tigress is Po's favorite of the Furious Five, even though throughout most of the first film she's the one in the group who is the most vocal about her disdain for him. It takes until the end of the movie for her to respect him. However, in the sequel, While not necessarily romantic (yet), the two share a lot of moments. When Po describes how confused he is about his past, and how Tigress wouldn't get something like that, she suddenly hugs him, much to the shock of the other Furious Five, and tells him she does understand. She then tells him that she can't watch her friend die, and to stay with Masters Storming Ox and Croc for his own protection. She also seems to be the most distraught out of the Five when Po is hit by Shen's cannon. Later, when Po returns and is about to get hit by Lord Shen's cannon, she pushes him out of the way. In the wreckage of the cannon-burst Po finds Tigress drifting and holds her hand briefly before pushing her out of harms way. After Po defeats Shen, he hugs her, with Tigress initially frozen shock before a smile grows on her face, while everyone else looks on in shock.
- Furthermore, when you are aware of the Tiger Versus Dragon of Chinese symbology, Po and Tigress' growing love is not just appropriate, it's almost imperative.
- To a lesser extent, there is Crane and Mei Ling in Secrets of the Furious Five, which the feline Action Girl is so nice and loyal to the bird in the All of the Other Reindeer situation that many fans like to imagine them having a romantic relationship while they are at it.
Aliens has quite a few, probably benefiting from the fact that they didn't have an official couple. The most obvious is Ripley and Hicks and Word of God has confirmed that James Cameron imagined the two of them and Newt becoming a family. Ripley also gets a bit of teasing with Hudson during the scene where he gives her his Badass Boast. She looks both uncomfortable and... slightly turned on. There's also a ton of subtext going on between Vasquez and Drake.
Dead Poets Society has some of this between Neil and Todd (shared glances, the "flying desk set" scene, Todd's reaction to Neil's death, et cetera.)