The first Final Destination had high school bully Carter calling protagonist Alex Browning by his last name due to their antagonistic rivalry. In an alternate ending where Alex dies saving his girlfriend, Clear Rivers, from the exploding car, Carter joins Clear (who is with her son Alex Jr.) at the cemetery. He is friendlier with her and the now-deceased Alex, referring to the latter by his first name.
Martin Riggs from the Lethal Weapon movies is always referred to as "Riggs", even though he calls his partner Roger Murtaugh by his first name.
Almost all of the characters in Alien and Aliens go by last names only. Ripley's first name (Ellen) was never stated in the original theatrical cut of either film, appearing only in a deleted scene from Aliens.
With the exceptions of Carter Burke, Ellen Ripley, Dwayne Hicks and (possibly) Gorman, all the marines in Aliens have their actor's first name for their real one (e.g. Al Apone (Matthews), Jeanette Vasquez (Goldstein), etc)
In most movies about military squads, characters are referred to by either their last name or a nickname. The Alien example above comes to mind, as well as Predator (except Dutch, of course) and Saving Private Ryan (his full name is James Francis Ryan).
All of the characters in The Thing (1982) only refer to each other by their last names. This is only averted after Bennings is shot and MacReady calls him "George".
You'd be hard-pressed to find anyone calling Richard B. Riddick by his first name in Vin Diesel's series of action thrillers. Also true for (William J.) Johns and (Carolyn) Fry.
In Pirates of the Caribbean Commodore Norrington's first name isn't even never mentioned in the first movie. Second and third movie reveal that it is James. Similarly, Barbossa's first name isn't mentioned until the third when Captain Jack Sparrow calls him "Hector," which is itself Ascended Fanon taken from an earlier interview with Johnny Depp and Geoffrey Rush when the former speculated on what Barbossa's name might be.
In Inception, the characters often refer to each other by their last names — the main character, Cobb, is only called by his first name by his wife and father/father in law, another character only goes by 'Eames', implied to be his last name (there's even a fanfic about this), and the team usually refers to Robert Fischer as just 'Fischer'.
The Way Back has Mister Smith, who refuses to give his first name and is simply called Smith by most of his companions. Some of the ones with a shakier grasp of English think 'Mister' is actually his first name, and the sole child in the group uses it like it is.
In the movie Waitress Jenna won't call the man she's having an affair with by his first name, even though Dr. Pomatter (Jim) uses hers.
Taylor in Planet of the Apes. His first name doesn't even pop up in the film, it was revealed later. Brent is this as well in the 'Beneath' sequel, which also has Mendez. It might not have been a last name but more of a title among the mutants by the time of the film, but it appears to have begun as a last name (see Battle) 'Conquest' has Mac Donald and Governor Breck. 'Battle' has another Mac Donald and Kolp.
Highlander had Ramirez, and sometimes Connor would just be called Macleod.
Blade Runner is an interesting case. The human characters are usually called by their last names and replicants by first names, which serves to reinforce the point of how humans in the film tend to act cdistant and impersonal, and the replicants are more emotional. This also foreshadows Rachael's status.
In The Shop Around the Corner, the shop workers all address each other as "Mr. _____" or "Miss _____". Kralik does start privately calling Miss Novak "Klara" once he begins to care for her, though.
In the first Ghostbusters movie, Ray Stantz almost exclusively refers to his colleagues by their last names, while everyone else uses given names. This seems more like personal preference rather than any indication of his relationship with them, however. In the sequel he seems to have moved on from using only surnames and has instead started nicknaming everybody (though he does use Winston Zeddemore's last name while he and Winston are under the effects of the negatively-charged mood slime and on the verge of killing each other and uses Egon Spengler's surname to refer to him in a much less emotionally charged moment).