All in the Family: Mike addresses his father-in-law as Archie (or "Awch"), while in contrast he always calls Edith "Ma."
In Arrow, most people refer to John Diggle, Oliver's badass ex-military driver and assistant (to both Oliver and the Arrow) as Mr. Diggle, Diggle, or Dig. But when going with him to help him out, Oliver calls him 'John' to stress how serious the situation is.
The early Season 1 episode "A Clubhouse is Not a Home," Mike – talking with his sons about sharing and getting along with their new stepsisters – refers to their stepmother as "Carol." Greg also calls her "Carol" when talking about her at one point in the pilot episode, "The Honeymoon." But it doesn't take long before she becomes "Mom" to them.
Season 2's "Our Son the Man" sees Greg attempt this on his parents, Mike and Carol. Mike immediately corrects his son.
In the Brady sequel TV series and movies, Marcia's husband, Wally Logan, always refers to adults – even his bosses and clients – by first name. This includes Mike and Carol.
After insistently calling Jaime "Kingslayer" ever since they met, Brienne displays her new-found regard for Jaime Lannister by calling him "Ser Jaime."
Littlefinger frequently reminds Sansa to call him "Petyr" to encourage some intimacy between them. She prefers to call him "Lord Baelish," which is still more polite than "Littlefinger."
Strangely, unlike most other lords in the series Tywin Lannister is usually referred to as "Lord Tywin" rather than "Lord Lannister".
Western Inversion: On Ned's Declassified School Survival Guide, most of the kids go by nicknames, and the kids who call them by their real name usually really like them. Lisa calls Cookie "Simon," Evelyn calls him by his last name "Cook," and Moze's boyfriend and fanboys call her "Jennifer." Once when she tried to get Ned to call her "Jennifer," he was physically unable to say it.
In Jekyll, Dr. Jackman's best friend turns out to be a spy planted into his life as part of an elaborate scheme. He attempts to appeal to Jackman's wife, Claire, by calling her name - who turns around and orders him very, very confidently to address her as Mrs. Jackman.
On Frasier, the Cranes would always refer to Daphne by her first name, and Daphne would address them as "Dr. Crane" or "Mr. Crane" without fail. This was a plot point in the episode where she accidentally found out about Niles' feelings for her. When the long-running Niles and Daphne romantic subplot finally came to a head, Daphne ran away from her wedding to be with Niles. He was waiting outside the chapel in a Winnebago. As Daphne climbs in, Niles tells her "Fasten your seatbelt, Daphne."
Daphne: Fasten yours, Niles.
She finally calls Frasier and Martin by their first names after she marries Niles.
Roz referred to Martin as "Mr. Crane" for the first one and a half seasons before switching to "Martin", but she always called Frasier and Niles by their first names.
Similarly in Cheers: Woody called Sam and Carla by their first names, but Diane and Rebecce were always "Miss Chambers/Howe", and the customers (Norm, Cliff, Frasier, Lilith) were always referred to as "Mr/Dr.....".
Which meant Frasier and Lilith were "Mr Dr Crane" and "Mrs Dr Crane".
Woody did avert this with Norm briefly by yelling "NORM!" when the clientele changed after Sam sold the bar and nobody else would do it.
Turk: Christopher? You only use my full name when you're angry, or when we're having sex. ...are you angry when we're having sex?
Played with when it turns out that Kelso thinks he is on a first-name basis with Turk.
Turk: You think my name is Turk Turkleton?
Moments where Cox actually calls JD by his name are often Crowning Moments of Heartwarming. The clearest case coming at the end of "My Fallen Idol", after J.D. helps to bring Cox out of his alcoholic stupor and Cox thanks him.
Another CMOH was the scene where the Janitor refers to Elliot as Elliot, rather than Blonde Doctor.
In the first season of 3rd Rock From The Sun, Dick and Mary mostly referred to each other as "Dr. Solomon" and "Dr. Albright" respectively. They shifted permanently to first-name terms after they hooked up at the end of the season.
The rest of the Solomons consistently refer to Mary as "Albright". In the Body Swap episode, Sally-in-Dick's-body had trouble remembering to say "Mary" instead of "Albright".
In Star Trek: Deep Space Nine, Jadzia Dax's long-standing friendship with her commanding officer, Benjamin Sisko, earned her the privilege of addressing him by his given name while on duty.
As the initially-antagonistic relationship between Chief O'Brien and Dr. Bashir develops into firm friendship, the two start addressing each other as Miles and Julian.
Meanwhile, Major Kira's first name - Nerys - was used only rarely, and usually signified a very close relationship, such as her friendship with Dax and her relationship with Odo.
Garak was called 'Garak' by everyone, but in his first spotlight episode we discover his first name is Elim. When Tain's housekeeper appears in one episode, constantly calling Garak by his first name, it not only stands out glaringly to the audience, but to Odo as well, who is extremely suspicious about why the housekeeper of the man who exiled Garak would have such affection for him. But that question is par for the course, given Garak's Mysterious Past. (In Andrew Robinson's novel, it was because she's Garak's mother.)
In Star Trek: The Original Series, Dr. McCoy never used "Captain" except when the situation was serious, otherwise he would use Jim and Jim would call him "Bones." He addressed him as "Leonard" only once, in "Friday's Child", and only because they were congratulating each other on the High Teer of Capella IV, Leonard James Akaar, being named after them (this is also the only time McCoy addresses Kirk as "James" instead of "Jim"). Spock, naturally, is the exact opposite of McCoy (and neither of them would have it any differently): Kirk is usually addressed as "Captain", but when Spock is subject to emotional instability, he's "Jim". He mellows considerably by the time of the movies, and almost always refers to Kirk as "Jim".
Scotty is almost always on a Last Name Basis with everyone, even though he himself insists on being called "Scotty". He is never addressed by his own first name, "Montgomery". Scotty addresses Kirk as "Jim" exactly once in three seasons.
Getting on a First-Name Basis with the Romulan Commander is a pretty important moment for Spock in "The Enterprise Incident."
Meanwhile, in Star Trek: The Next Generation, Jean-Luc Picard's more aristocratic style of command meant that only longtime friend Beverly Crusher ever referred to him by his first name (aside from recurring antagonist Q, but there were... otherreasons for that one. And Riker, in the episode where he was briefly turned into a Q; Picard promptly called him on it.) Data, Worf, and Geordi, however, were referred to by first name even while on duty (albeit in part because Data only has one name and Worf, though Happily Adopted, uses the Klingon Patronymic "Son of Mogh" rather than his parents' surname of Rozhenko). Picard will also switch off how he refers to the crew depending on whether it is a formal or informal situation. When acting as Captain Picard, he says Mr. Data, Mr. Worf, Dr. Crusher. When informal or more personal, he used first names, particularly with, as above, Beverly, who he's known for like two decades. Will Riker gets the nickname of "Number One" on duty unless it's a full-formal situation.
Troi and Riker almost always informally call each other Deanna and Will, although they were in a relationship previously and are very close friends.
When called by first name, Riker is always called Will, never William. Even the stiffly formal Captain Jellico (when temporarily filling in for a missing Picard) upon introduction asks Riker whether his preference was Will or William.
The Even More Mildly Military crew of Star Trek: Voyager were referred to by first name almost all the time, with only two exceptions: Janeway, who was The Captain, and who only gave this privilege to Chakotay; and the Doctor, who had no name besides "The Doctor." Of course, even after Chakotay gets upgraded to First-Name Basis, it's hard to tell because "Captain" and "Kathryn" sound so much alike.
Star Trek: Enterprise. When Daniels, Captain Archer's steward, reveals that he's a time-travelling agent from the 31st Century he starts calling the captain "Jonathan" without being invited. Silik, his opponent in the Temporal Cold War, also calls Archer 'Jon', likely for the same reasons — as a patronising way of indicating that he's completely familiar with him (due to his knowledge of the future). Archer himself refers to his bridge crew by first name even while they're on duty—Hoshi and Trip are old friends, but this isn't so for the rest. However, when Ensign Reed questions his tendency to invite various crewmen to dinner, Archer explains his belief that rigid formality would be a liability when they're basically alone in deep space, and he'd rather they be more like True Companions than a military crew, and the first-name basis would fall into that.
McGee and Gibbs on NCIS go by their last name (or by the nicknames "Probie" and "Boss," respectively). Abby is about the only person to call McGee by his first name with any regularity, and Ducky is one of the few who can get away with calling Gibbs by his. Ducky nearly always addresses the other members of the team by their full first names - "Anthony", "Timothy", "Abigail", "Eleanor" etc.
Jethro is actually Gibbs' middle name. His first name is Leroy.
24 featured a rare negative usage of this trope: in Day 5, when Special Agent Aaron Pierce discovers President Logan was involved in the day's conspiracy, he is captured and the President tries to convince him to remain quiet or be killed. What follows is probably Pierce's Crowning Moment of Awesome:
Aaron Pierce: There is nothing that you have said or done that is acceptable to me in the least. You are a traitor to your country and a disgrace to your office. And it's my duty to see that you are brought to justice for what you have done. Is there anything else... Charles?
This could be considered a Crowning Moment of Awesome for both Aaron Pierce and his actor, Glen Morshower: the scene was done in a single take. The director thought Morshower's delivery to be so perfect that no further shooting was necessary.
There's also an instance of first name basis being revoked, when Mike joined the others who were trying to undermine Palmer. When Mike calls him David afterward, Palmer lets him know it's "Mr. President" now.
Ethan Kanin, implied to be an old friend of President Taylor, is the only one to call her "Allison" on the show. To everyone else, she's "ma'am" or "Madame President."
Stargate Atlantis: Most people address John Sheppard by his first name. However, Rodney MсKay never until the first episode of season 4 called Sheppard by his given name. And after that he calls Sheppard by the first name only in very dire situations. Teyla regularly uses John's last name and/or rank. When he suggests using John, she does it once and then quickly returns to Sheppard or Colonel, unless the situation gets really serious.
Elizabeth and John start off with a very formal 'Doctor Weir' and 'Major Sheppard'. A few episodes in they use last names when talking about each other but first names in actual conversations. Halfway through the series they're using first names in front of anyone and everyone. Oh, this includes enemies who have invaded Atlantis or kidnapped John. Like this exchange:
Koyla: "I think you underestimate the sympathetic nature of Doctor Weir."
John: "And I think you underestimate Elizabeth".
(Yes, John if you want to avoid being used as bartering chip try not to flaunt how close you and the expedition leader are, while captured and at the mercy of your arch-enemy.)
Everyone calls Ronon and Teyla by their first names.
Stargate SG-1 is fairly complicated here. Daniel and Jack call each other by their first names from the get-go. Besides Daniel being a civilian, they bonded pretty solidly in the movie. Teal'c doesn't even have a surname. Samantha Carter usually addresses Jack as "Colonel", and Jack calls her "Carter". It's only during the rare intense UST moments (see "Lost City") that Sam calls him "Jack".
When Mitchell comes along, he and Daniel initially invite each other to use their first names. They never do. Mitchell and Jackson are strictly Last Name Basis, while Sam and Cam use first names. Everyone is on First-Name Basis with Vala, except Teal'c, who is Full-Name Basis with everyone.
Farscape examples: At first, Aeryn and D'Argo call John "Crichton". When he becomes closer to them, they switch to "John". Also, at first Pilot calls Aeryn "Officer Sun". Only later does he start to call her "Aeryn".
Oddly, in "The Choice" a grief-stricken Aeryn shouts "Crichton!" repeatedly off a balcony, not John. One explanation is that due to the death of the version of Crichton she had entered into a relationship with, she was conflicted over her feelings for the other version of Crichton who was still alive, who both was and wasn't her "John".
Scorpius has a tendency to refer to Crichton by his last name when talking to others, whilst insisting on "John" when speaking to him directly. It's implied that he does so partly because he wants to appear Faux Affably Evil and partly because he wants to unnerve him.
Name usage on Lost is quite complicated (see also Last Name Basis.) Switching from someone's last name or nickname to a first name is a sign of camaraderie. As Sawyer's character has developed, more characters have begun calling him James. By season 5, nobody calls him Sawyer anymore. Similarly, most of the cast moved from "Hurley" to "Hugo" over the course of the seasons (particularly interestingly with Ben, who originally called Sawyer and Hurley by their real names as part of his manipulative personality, and then ended up switching sides and becoming Hurley's second in command, and calling them their first names out of affection (or whatever counts as affection for Ben).) When Juliet Heel Face Turns from Others to Losties, she switches from last names to first names.
Despite the professional setting, every single character on The West Wing is called by their first name, with the exception of President Bartlet (who is called "Mr. President" or "the President", referring to him as "Bartlet" is usually a sign of contempt) and Mrs. Landingham, who is called thusly only because she used to be a secretary at the President's school when he was a kid. CJ is usually always called by everyone by her nickname, instead of her rarely-heard first name "Claudia Jean", though the President is, as usual, the exception.
The only two people to call President Bartlet by his name (Jed) are his wife, Abbey, and his Chief of Staff, Leo. It's especially poignant in "He Shall, From Time to Time" when Leo finds out about the MS. He yells at Bartlet "Of all the things you could have kept from me, Jed!", and all Bartlet can say in return is "you haven't called me Jed since before the election".
That's the only time Leo ever calls him Jed. There are two other precision Jed strikes in the series. The first is in "Take This Sabbath Day," when Bartlet's childhood priest comes to see him at the end of a day in which he's decided not to commute the death sentence of a criminal. He asks if he should call him Jed or Mr. President; Bartlet asks for Mr. President because it helps him think of himself "not as the man, but as the office." The priest complies, and the scene proceeds with him lecturing Bartlet for acting like whether to execute someone was a tough call for a Catholic. Bartlet gets the note telling him that the man has been executed, and the priest says, "Jed, would you like me to hear your confession?" The other time is "Ellie," with the surgeon general, who is an old family friend and godmother to one of his daughters (Ellie of the title), talking to him about his relationship with her.
Charlie initially addresses Zoey as "ma'am", despite Josh telling him it sounds awkward. He asks if he can address her by her first name, and she says he can if she can call him by his.
The members of the BAU in Criminal Minds mostly use last names with each other, with some exceptions:
Rossi is the only other person besides Hotch's ex-wife to refer to him as "Aaron". This begins with Rossi's very first episode, "About Face", and is a means of showing right from the get-go that the two of them have a previously established working relationship.
Similarly, while other characters have occasionally referred to or addressed Rossi with "Dave" or "David", Hotch is the only one who calls Rossi by his first name with any regularity.
JJ is always called by her nickname, almost never "Jareau" or "Jennifer".
JJ and Gideon are the only ones to call Reid "Spencer" (other than his parents).
Morgan and Garcia keep it professional most of the time - well, as professional as Morgan and Garcia get - but during times of extreme stress ("Penelope", "Mayhem") or when they're being extremely honest ("Hopeless"), they will call each other "Penelope" and "Derek".
A reversal happens when Morgan takes Hotch's place as leader of the BAU. He stops in the middle of calling her "baby girl" and switches to "Agent Garcia".
Elle was always called by her first name, rather than "Greenaway," with almost no exceptions.
Most members of the team, other than Hotch, switch between calling Emily Prentiss by her first and last name at random. Occasionally, they call her "Em."
Though "Emily" has been used with increased frequency from season four on, particularly by Rossi.
Rossi is the only person in the world who can get away with calling Section Chief Strauss "Erin."
Which can occasionally lead to confusion; everyone pronounces Aaron as Erin, so if both are in a scene and Rossi calls one of them by name...
It's also interesting to note that Strauss tends to return the favor, frequently calling Rossi by his first name, too. She occasionally uses 'Agent Rossi,' particularly when they're in a public situation, but she's called him 'Dave' enough times, possibly even more consistently than Hotch.
On That '70s Show, Jackie started calling Steven Hyde on his first name after she became interested in him.
Fran is thrilled when Maxwell finally starts using her first name because it shows he's acknowledging their growing romance.
On M*A*S*H, Hawkeye expressed his disdain for military protocol by, among other things, routinely addressing Colonel Blake as "Henry", Major Burns as "Frank", Major Houlihan as "Margaret" (or, in earlier episodes, "Hot Lips"), and Major Winchester as "Charles". Only once, however, did he address Colonel Potter as "Sherman" - in an episode where he and the others are trying to convince Potter to stay at the 4077th after he starts to believe he's not needed and announces he's considering an early retirement - and this occasion is unsurprisingly one of the show's Crowning Moments of Heartwarming.
In an episode of Psych where Shawn spends most of the episode captive, Lassiter starts referring to the detective by his first name (having previously stuck to using his last name only) when he learns that Shaun has not only been taken captive, but shot. Once the episode is over, Lassiter goes back to using the derisive "Spencer" title, but the first name usage demonstrated how concerned he was for Shawn's safety. Lassiter later provides another example of the trope in the same episode, when he gives Shawn a congratulatory "Good work, detective", although he denies having done so to Shawn an instant later.
In a variation, on The Sarah Jane Adventures, Sarah Jane Smith insists that her friends call her "Sarah Jane" — except for the Doctor, who alone reserves the right to call her "Sarah".
However, considering the age difference, the fact that they call her "Sarah Jane" instead of "Miss Smith" is significant.
Detective Elliot Stabler is usually "Elliot", though the other detectives will call him "Stabler" occasionally. Both his partner and his wife, and no one else, call him "El".
Detective Odafin Tutuola is always called "Fin" by everyone, because his real name is a bloody mouthful. No one ever calls him simply "Odafin". Fin usually uses last names, except with Benson and Stabler. Even his partner of many years is almost always just "Munch".
Detective (later Sergeant) John Munch is always called "Munch" by everyone (because why wouldn't you?), with the sole exception of Cragen, who usually calls him "John".
Captain Donald Cragen is always addressed as "Captain" or, more affectionately, "Cap"; they call him "Cragen" when he isn't around. The only regular who ever calls him "Donald" or "Don" is Alex Cabot. Cragen usually refers to everyone by their first name; these customs are befitting of his status as Team Dad.
Dr. George Huang is always "Doc" or "Huang"; no one calls him "George" except for, once again, Alex Cabot. He refers to most people by their first names.
Dr. Melinda Warner is "Melinda" to Benson and Stabler; likewise, she calls them "Olivia" and "Elliot". To everyone else, she's "Warner", "Doc Warner", or simply "The M.E."; she, in turn, tends to stick to titles.
The ADA is always her first name, apart from the despised ones, who are "Greylek" and "Paxton". Alex Cabot, in particular, would refer to everyone by their first name, even when they weren't around. However, Rafael Barba is well-liked but still called "Barba" or "Counselor" instead of "Rafael" by just about everybody.
On The Mentalist, the fact that Bosco and Lisbon call each other "Teresa" and "Sam" ought to tell you something. The significance wasn't revealed until Bosco was dying - they were in love.
Used in Bones frequently. When Cam first arrives, she calls Zach Addy and Jack Hodgins by nicknames (Zacharoni and Hodge-podge, respectively) to indicate that she's already close to the team. She calls Booth by his first name to show that she has a romantic history with him, which continues throughout the series. Brennan refers to Cam as "Dr. Saroyan" for a while, but eventually falls into calling her Cam when they become friends.
One episode demonstrates Brennan's conflict between being Temperance (her first name, which only her father and brother call her by) or Dr. Brennan when her father is on trial for killing a man. Booth, who always refers to her as Bones, seems to have neatly solved that problem. Booth himself is always called by his last name except by his brother, his ex, and Cam.
Everyone calls Angela by her first name, although it's eventually revealed that Angela isn't her birth name. She occasionally calls Hodgins "Jack," but he's almost always called by his last name.
It's pointed out that Brennan calls the interns Mr/Ms LastName to highlight that they're not doctors yet. Other people tend towards calling them by their first names.
Everyone calls Sweets by his last name except Daisy, who calls him Lancelot. (His first name is Lance.)
Murdoch will occasionally address Constables Crabtree and Higgins by their first names, but he generally addresses others as "Constable" or by their surnames (such as "Jackson" or "Hodge"). This seems to denote the closer relationships he has with them, particularly in Crabtree's case. Rank may also have something to do with it, since he never uses Inspector Brackenreid's first name, but always either uses "Sir" or Brackenreid's title. Brackenreid always calls his detective "Murdoch" or the endearing phrase "me old mucker" and never uses "William".
Detective Murdoch and Dr. Ogden tend to address and refer to each other by their titles in professional settings when strangers are involved or on business matters, and they revert to first names when discussing personal matters. Among other things, Murdoch seems sensitive to the need to underline the coroner's professional credentials for people who might be wondering what a woman is doing asserting authority at a crime scene.
The first time Dr. Grace is giving Murodch a briefing (with Dr. Ogden), she notices Murdoch calls her mentor "Julia" and he corrects himself. Julia doesn't seem to mind.
Murdoch is observing Crabtree interrogating a culprit near the end of "War on Terror" (a first for the constable) when Dr. Grace stops by and joins him at the window. She calls George by his first name, and it's Murdoch's turn to notice the sudden familiarity. Later in the morgue, she tells George to call her "Emily" and they discuss the meanings of her first name.
Done rather comically on House in the first season when Cameron reads an "empowerment at work" book and begins to call Foreman and Chase by their first names. They respond by saying her first name whenever they say anything at all to her.
Cameron: Are you mocking me?
Foreman: No... Allison.
When Chase and Cameron are together they call each other by their last names at work and their first names whenever else.
In the BBC show Sherlock, which puts Sherlock Holmes in a modern setting, the two main characters call each other Sherlock and John, rather than Holmes and Watson.
Moriarty introduces himself as Jim. Both times.
In ''Monk', Adrian Monk only calls Captain Stottlemeyer "Leeland" when he's especially concerned for him.
When Sheridan and G'Kar are saying farewell to each other (as G'Kar is about to leave the station to go exploring), Sheridan reflects on their sometimes frustrating but ultimately respectful friendship. As he turns to leave, G'kar quietly says "Goodbye, John", which Sheridan points out is the first time G'Kar had ever called him by his first name. G'Kar denies it, leading to one last, brief argument between them before both smile and laugh and say goodbye again.
While they call each other "Captain" and "Ivanova" on duty, off it Sheridan and Ivanova call each other "John" and "Susan" due to their long-standing and incredibly close friendship.
In the same fashion, it's a significant moment when Sheridan and Delenn go from "Captain" and "Ambassador" to "John" and "Delenn".
The eponymous Inspector Lynleyalmost universally called his partner, Detective Sergeant Barbara Havers, either 'Sergeant' or 'Havers' while on duty. It's not until the last produced episode of the show that he switches to calling her 'Barbara' on a regular basis, only calling her 'Havers' when he is cross with her; this marks a significant shift in their relationship. (Havers, however, calls him nothing but 'Sir', relying on tone to get her point across, as he is both her social and professional superior.)
Kamen Rider Fourze protagonist Gentaro Kisaragi refers to almost all his classmates by just their first name, no honorific. In Japan, this is considered very intimate, the sort of thing only really close friends or lovers would do, but Gentaro does it because he wants to be friends with everybody. A few members of the Kamen Rider Club, such as Lovable Jock Shun Daimonji, do the same with him.
Used in Castle with everyone in the precinct, including Castle, except for highly emotional moments. Becket calls ME Lanie Parish by her first name all the time to show they are long time friends. Det. Ryan and Esposito refer to each other by last names, though Ryan started referring to Esposito as Jav or Javier around the third season. Castle's mother and daughter are primarily referred to as Martha and Alexis, respectively.
In Supernatural, Sam, Dean, and many other characters call the usually-immortal, sometimes-God, very powerful Angel of the Lord Castiel "Cas"
on the original, Grissom calls all the team by their first names. He is the exception,everyone,even his GF/wife calls him Grissom. DB,on the other hand,is just DB to everyone,or "Russell" rarely. Finn is an exception,she hates "Julie" or "Jules",DB's nickname for her. Brass and Ecklie were exceptions, also, though several characters-mainly Grissom and Catherine-didn't hesitate to use "Conrad" sometimes. Gil would sometimes call Brass by his first name as well.
On CSI NY it varies. First names are most common, except with Hawkes and Flack. Mac uses both, usually using first names with those two when he's concerned. Danny also makes exception with Lindsay, naturally - he calls her "Babe" as often as her name. ("Montana" is rare these days.)
CSI: Miami was also mostly first names,though Eric got called Delko sometimes. and Horatio was often "H". Horatio also made an exception with Ryan,often calling him "Mr.Wolfe".
In season 4 of Boardwalk Empire a series of reveals shows us that Warren Knox is Obfuscating Stupidity and is someone to be concerned with. In the second episode, we find out that he and J. Edgar Hoover are good friends and he freely calls the Acting Director of the Bureau of Investigation "Edgar" even in a professional setting.
Mrs. Marian Cunningham from Happy Days was the only person allowed to call Fonzie by his given name of Arthur.
The Tudors: Only Catherine of Aragon, Thomas More and Charles Brandon ever address Henry VIII as "Henry" rather than "Your Majesty".
Over the Third Doctor era of Doctor Who, the Doctor always referred to Brigadier Lethbridge-Stewart by his rank. Come his regeneration into the Fourth Doctor in "Robot" and he begins referring to him as 'Alistair', which clearly perturbs the Brigadier.
On The Bob Newhart Show, Bob generally calls his patients by their last names, but refers to Michelle Nardo by first name.
In Wolf Hall, Thomas Cromwell is almost always Cromwell, and if it's someone who's close (or Henry in affectionate mode) it's shortened to Crumb. The only person in his professional life who routinely called him Thomas was his mentor and Parental Substitute, Cardinal Wolsey.
In an early episode of X Company Aurora asks Alfred why he never calls her by her name, and he responds that he's afraid of how it would taste (Alfred has Synthesia which causes his senses to be fused). In the second last episode of season two, he calls her Aurora. They kiss soon after.
Pretty Guardian Sailor Moon uses this as a plot point in an early episode. Ami starts calling Usagi by her first name (making a direct leap from "Tsukino-san" to "Usagi") in an attempt at making friends. However, it soon becomes clear that Ami's putting undue stress on herself by moving too fast. However, Ami then learns An Aesop about true friendship and from that point on comfortably uses the "chan" honorific.
In the early episodes of The X-Files the protagonists always refer to each other as "Agent Mulder" and "Agent Scully". Although they remain on a Last Name Basis for the rest of the series, the dropping of these titles show they're beginning to accept each other as partners. More on Scully's side than Mulder's; Mulder drops the "Agent" quickly into the pilot, whereas Scully calls him Agent Mulder until the second episode.
Scully only ever tried calling Mulder "Fox" once and was informed that he liked "Mulder" better, so she never tried again. Mulder called Scully "Dana" when he was especially concerned about her, or when they were having a particularly intimate moment (not necessarily like that, pervs) during the first few seasons. But by around season 4, even that had stopped, as if the last names had become more intimate by that point. In the second movie, set six years after the series, they've been living together the whole time and they're still on a Last Name Basis.
However, Mulder does tend to call her "Dana" around her family; Scully only meets with Mulder's mother once and does not refer to Mulder by any name.
In contrast, Doggett and Reyes call each other by their first names, usually only addressing each other by "Agent Doggett" or "Agent Reyes" around other agents.
Scully winds up on a sporadic first name basis with them both in season nine, though more often with Reyes than Doggett.
Trip Tucker has been friends with Captain Archer for years before Enterprise was launched, but always refers to him as Captain, even when off-duty.
Archer often calls his crew by their first names - Hoshi, Travis, Trip, Malcolm - but Malcolm Reed, the extremely uptight, formal British armoury officer, never calls anyone by anything other than their rank or rank + last name, even when off duty. By the fourth season, the fact that he starts calling Commander Tucker "Trip" is a sign that he's defrosted a little and become properly comfortable with their friendship.
In House, virtually none of the doctors on staff are referred to or addressed by their first names. Only the title character's parents and his ex-girlfriend (and on one occasion, Wilson) call him "Greg." None of the central cast ever calls Dr. Wilson "James" ? not even his best friend, Dr. House (although he will sometimes use "Jimmy" condescendingly) ? nor does anyone call Dr. Cuddy "Lisa." Only on rare occasions does anyone ever call Drs. Cameron, Chase, and Foreman "Allison," "Robert," or "Eric," respectively. On one occasions, Dr. Cameron starts addressing her colleagues by their first names (and House as "Dr. House" instead of merely his surname) as a strategy aimed at making them take her more seriously, which Dr. House immediately points out.
This tradition continued once House assembled his new team, as well; you'd be hard pressed to find anyone who called Drs. Taub and Kutner "Chris" or "Lawrence", respectively. This was taken to an extreme with Dr. Remy "Thirteen" Hadley, who was called simply "Thirteen" for an entire season after her introduction.
Despite all being good friends, the male teens from That '70s Show only ever refer to each other by their surnames. Donna also does this, except for her boyfriend Eric.
Eric's mother Kitty calls everyone by their first names (except Fez, but he has No Name Given) While Red uses their last names but will occasionally use their first names if he has something important to say.
The characters on Are You Being Served? nearly always refer to each other as "Mr." or "Mrs./Miss"; to the point that the rest of the staff has to do some detective work to figure out what Mrs. Slocombe's first initial stands for, and you have to watch several episodes to find out everyone's first name.
Monty Python has an entire sketch based around an interviewer calling his subject by his first name, and then takes it Up to Eleven as he begins to use names such as "sweetie pie" and "pussycat".
Sir Edward: I don't like being called "Eddie baby".
Pushing Daisies has a slightly goofy example, in an episode featuring the magician The Great Hermann. When they get to know him better, he tells them they can call him "Great."
In Flight of the Conchords, the Prime Minister of New Zealand is always referred to as "Brian," rather than by his last name or any honorifics, one of many jokes painting New Zealand as a backwater.
Kaamelott: The series uses a particular quirk of the French language: Everyone uses first names, but using the more formal second-person form of 'you' (and rank if they feel slightly less insulting than usual, like "Sir Lancelot"). Even the pairs of Those Two Guys use it despite being best friends. The only one who uses the first-person form is Elias, an actually competent mage who uses it as a passive insult towards Arthur.