At the end of the Kim Possible movie So the Drama, Dr. Drakken, the Big Bad, finally remembers the name of Kim's sidekick; throughout the show, he always referred to Ron as something along the lines of "the buffoon whose name escapes me."
Most of the operatives on Codename: Kids Next Door refer to each other by number. If two refer to each other by first name, it's safe to assume they're particularly close (Numbers 3 and 4 call each other "Wally" and "Kuki" all the time) or the moment is particularly deep (Number 1 calls a discouraged Number 362 "Rachel" when she's ready to give up her job as Supreme Leader).
In the early episodes of Gargoyles, Goliath always addresses Elisa Maza as "Detective", though he does refer to her by name when she's not around. Later in the show, as their relationship develops into a more romantic one, he becomes more and more comfortable calling her by her first name. Of course, none of the other gargoyles have this problem; the younger ones call Elisa by name from the get-go, and Hudson usually refers to her as "lass".
Though it's a bit different here, as it's shown early on that gargoyles traditionally don't have naming conventions, or names at all, like the way the humans do (Goliath and Demona were originally the only two with names, and the others got them early on, and only out of convenience for Elisa rather than any attachment to a particular name).
In Code Lyoko, the Prequel episode reveals that Jeremie and Ulrich went through this during their first adventure. Prior to X.A.N.A. getting involved, they barely knew each other and addressed each other by surname.
On The Fairly Oddparents, an episode revealed that Crocker was friends with his current boss, Principal Waxaplax, in their childhood. During this time Waxaplax was in love with him. This ended with his claims of fairies in college, which got worse over the years. By the time he was starting his teaching job, Waxaplax was demanding to be called by her last name.
Regardless of how romantic they get, Fry and Leela never refer to each other by their first names (Philip and Turanga, respectively).
It's tricky on Leela's part, since Leela's "first" name is her family name — her parents are Turanga Morris and Turanga Munda, but it's unknown if Leela was aware of the naming order since she was "abandoned" at a ophanarium and didn't meet her parents until some two decades later, and the viewers weren't clued in on it until they were introduced, so for a while it was thought Turanga was her first name. Regardless, he's still referring to her by her given name, so that's not as strong an example. Fry, however, is.
Up until "The Problem With Popplers", Fry didn't know Leela's family name, and Bender didn't know Fry's given name.
There was also an episode with a past girlfriend coming to the future who only referred to Fry by his last name. It seems to be that the only people who called him Phillip were his parents and brother.
Professor Farnsworth is usually called "Professor" by Fry, who is his great great great etc. uncle. Pretty much the only one who gets to call the Professor "Hubert" is Mom. Rarely, Zoidberg also calls him "Hubert" after it was established that the two have been friends for decades (and on very rare occasions, the Professor has called Zoidberg "John").
There was an episode of The Simpsons where a Straw Feminist comes to the school after Skinner made a sexist remark. While talking to her, Chalmers uses her first name and she replies that it's a form of harassment (Is it?) so he decides to go all out and kiss her.
Without having seen the episode in question, the Straw Feminist may have a point: It's generally polite, when speaking to an authority figure, stranger, etc., to use the surname, especially to a man. People have the tendency to refer to women by their first names (Hillary Clinton becomes "Hillary" instead of "Clinton" or "Mrs. Clinton", for example) and it's uncommon for adults to refer to children the same way. Bring in old patriarchal notions regarding men, women, children, and their roles in the home, and you can see how some women feel that First Name Basis is treating them like children, or otherwise of a lower status.
A completely non-romantic example is present in "Two Bad Neighbors", between Bart and former President George H.W. Bush.
Bush: You know, in my day, little boys didn't call their elders by their first name. Bart: Yeah? Well, welcome to the 20th century, George. Bush: I'll kick you right out of the 20th century, you little...
In "Who Shot Mr. Burns?" Burns and Smithers have an exchange where they call each other "Waylon" and "Monty." Since they always refer to each other by last names only, this was probably to emphasize how personal it was when Burns fired Smithers shortly thereafter.
Subverted with Professor Utonium and Ms. Keane on The Powerpuff Girls, as neither character's first name is ever disclosed. The girls themselves are mentioned by first name only but never suffixed with Utonium.