In Pirates of the Caribbean, Elizabeth is furious that Jack refers to her by her first name during their first encounter - "It's Miss Swann!". Will refuses to call Elizabeth by her first name, despite their knowing each other as children, because of their difference in social status; when Elizabeth accepts it and calls him "Mr. Turner", he is deeply grieved. Later, Jack calls Elizabeth "Captain Swann" to acknowledge (with some difficulty) that she has one of the pieces of eight; Bootstrap Bill calls his own son "Captain" and Will calls his own father "Mr. Turner" to acknowledge their roles on the ship; and Barbossa calls Elizabeth "Mrs. Turner" to acknowledge her marriage (though this one is a callback to the first movie, where Elizabeth passed herself off as Elizabeth Turner). Such careful usage was not common in the movies.
Nero in Star Trek consistently uses first names, apparently to show his contempt for his opponents. For example, consistently referring to Captain Pike as 'Christopher'.
At the beginning of the movie Nero asks about "Ambassador Spock," which is about as formal as possible since Spock only has one name. He's probably trying to be polite, at least until he finds his opponent doesn't have the information he wants, as well as foreshadowing the Time Travel plot twist.
Also invoked by Uhura, since Spock is the only one with whom she is on a first name basis.
Spock calling Kirk "Jim" for the first time is a turning point in their previously antagonistic relationship.
In Star Trek Into Darkness, when Scotty resigns in protest over the missiles, he makes a last appeal for Kirk to reconsider and calls him "Jim".
In Ever After, Prince Henry asks Danielle to call him "Henry" after he falls in love with her. Then he painfully reverses the trope later on: "Do not address me so informal, madam. I am a Prince of France — and you are just like them." Later, when they've decided they really do love each other, the prince calls Danielle by her name for the first time, instead of the alias she used for half the movie.
In the X-Men films, just like in the comics, Charles Xavier (Professor X) and Erik Lehnsherr (Magneto) always use their first names when speaking to or about each other. Only a handful of others are on a first-name basis with them.
In X-Men: Days of Future Past, while the public and most other characters refer to Erik (Magneto) and Raven (Mystique) by their mutant code names, Charles and Hank still remain on a first name basis with both of them, and vice versa. This is also presumably true for Alex, who still addresses his former allies as Raven and Erik.
Surprisingly, the elderly Magneto calls Bobby by his first name instead of his codename (Iceman). This indicates that Erik must have gotten to know Bobby on a more personal level during their war against the Future Sentinels.
Lampshaded by the Captain of the submarine in Ice Station Zebra, who explains to a passenger that on such a small vessel it's more comfortable to call everyone by his first name. "My first name is Captain."
In GoldenEye, Janus actually addresses Bond as "James" instead of "Mr. Bond," which is rare for a James Bond villain. Though it's justified, since he and James are old buddies.
The Bond girls also normally call him "James". (all the other characters refer to him as Bond, Mr. Bond, or 007)
The Enforcer. Dirty Harry is partnered with a rookie female officer who's naturally defensive about any attempt to patronize her — so much so that "Don't concern yourself, Inspector" becomes her Catch Phrase. Her Famous Last Words as she dies in his arms are "Don't concern yourself...Harry."
Indiana Jones and the Last Crusade. It's an important moment when Indiana's father addresses him by name for the first time, having spent the entire movie calling him "Junior". And not just his given name (which they share), but the one his son has chosen for himself.
Doc Hudson's real name is Hudson Hornet. Guess what car he actually is!
Pepper Potts: Phil! Tony Stark: Phil? Uh, his first name is "Agent".
Note that it is completely in character for Pepper to learn his name, and for Tony to not. This gets a Call Back after Coulson is killed by Loki.
Tony: And there's one other person you pissed off. His name was Phil.
It is a point brought up by Pep Strebeck to Joe Friday in Dragnet that friends call each other by first names.
The only character in Back to the Future to address Doc as "Emmett" is Clara Clayton, his love interest.
EVERYONE in The Room- nobody seems to have a last name (Except possibly Chris-R, but who knows what that stands for)
In Pacific Rim, Herc always addresses Pentecost as "Stacker", given that they were contemporaries.
In The Guns of Navarone Colonel Andrea Stavros insists on going by his unadorned first name, in spite of outranking everyone else in the team. This is a confirmation of two things; that the Greek army is disbanded, and that he defers to Captain Mallory and Major Franklin since this is an Allied operation.
Oddly enough, the Hutts in Star Wars are on First Name Basis with everyone, despite the fact that they consider all other races inferior. For example, Jabba's full name was Jabba Desilijic Tiure, but everyone simply addressed him as "Jabba the Hutt". This seemed common for all Hutts.