A character is extremely territorial about where he sits: a favourite chair, spot on The Couch, park bench, or whatever. Either they never sit anywhere else, no one else is allowed to sit there, or often both.
This can develop, as on Friends, from characters always sitting in the same place out of necessity in a Three Cameras show, and eventually having their relationship with that spot lampshaded.
Alternatively it can be an ordinary character trait, possibly a kind of Security Blanket for a character with Super OCD. In a military (or Mildly Military) setting, the commanding officer ordering someone out of his chair can serve as an assertion of authority.
If the character dies, do not expect that chair to be filled any time soon.
Not to be confused with This Is My Side, a stock sitcom plot where a shared space is split down the middle. Should the two tropes ever meet, expect the chair's owner to find himself cut off from using it (or to try declaring it an enclave within his enemy's territory).
By that point, Pike had already promoted him to First Officer (while Spock is the Acting Captain). Still not a reason to sit in the captain's chair while Spock is on the bridge.
Inverted in the sequel, where Sulu is reluctant to sit in the chair when given temporary command. He does prove himself to be capable.
In The King's Speech speech therapist Lionel Logue (Geoffrey Rush) disrespectfully sits on the Coronation Throne in order to provoke stuttering King George VI (Colin Firth) into an outburst of indignation.
In Men of the Otherworld, Clay always kicks Logan out of Jeremy's chair, since Clay feels that respecting the Alpha's chair is a symbol of respecting the Alpha's territory and Clay is Jeremy's dragon. It's a longstanding issue between the two of them, to the point where Logan will vacate the chair as soon as Clay enters the room.
Septimus Heap: Marcia Overstrand is very vocal at insisting that her chair in the Wizard Tower is in fact hers.
Live Action TV
In the pilot of Star Trek: The Next Generation, the fandom rejoices as Capt Picard yells at Wesley to "Get out of my chair!" Reportedly, Patrick Stewart would behave in a similar manner towards reporters and others who sat in the captain's chair on the Bridge set without invitation.
This is deliberately averted on a couple of occasions; Q sits in the Captain's Chair as a sign of his own ego and contempt for humanity, and Picard has to stop his bridge crew who instinctively move to throw the omnipotent prankster off it. After Picard is assimilated by the Borg, Riker becomes captain. He's in the ready room looking at Picard's chair and wondering "What would you do?" Guinan then enters the room and sits in the chair, making the point that he's got to forget Picard and start thinking what should Captain Riker do.
As mentioned, the Central Perk sofa on Friends. One storyline even revolved around a pair of bullies kicking Ross and Chandler off it.
Another example is Chandler's single-episode Compressed Vice of getting extremely territorial over chairs he's recently got up from.
Another episode of Friends had Phoebe and Rachel forced to sit by the window because somebody got to their normal seat first, Rachel was quite angry. Of course this was a set up so the pair could see Ross "attacking" two women.
One episode's Couch Gag has the group walk in the Central Perk, find the sofa is already occupied and decide to simply leave.
Arch, I been waiting five years to say this: Get outta my chair!
Said chair later officially becomes "Archie's chair" when he's at the Stivics' house. For exceptionally noted house guests (Sammy Davis Jr., for example) Archie insists that they sit in his chair and he takes Edith's, relegating her to the sofa. Archie's chair is now in the Smithsonian Institution. It was sent there after CBS ended the series the first time — the producers then had to re-create the chair when they decided to continue.
How I Met Your Mother: The main characters always sit in the same table in the bar they always visit, so much so that it is "their" table and the bartender once threatened a group of extras who unknowingly sat there. A one-off gag has the gang walking in to find people sitting there;
Ted: Get out of our booth! Go!
The Royle Family: Jim always sits in the armchair opposite the TV, Denise and Dave on the sofa next to Barbara, and Anthony on a chair.
If Twiggy's round, he's in Anthony's chair, if Nana's round, she's next to Barbara. They even always sit in the same places at the dinner table. Not out of OCD or pure comedic purposes of any kind, the show just emulates the completely standardised ways that families interact with each other.
Cheers: Norm Peterson always sits on the same stool at the end of the bar. All of the regulars respect his claim to it (although Cliff calls dibs on it one time when it looks like Norm might not be coming to the bar any more), but in one episode some people new to the bar sit in Norm's spot and the stool next to it.
Norm: Um, excuse me, I was sittin' there...
Man: Oh, there was no one here when we came in.
Norm: No, I mean yesterday...and really since the Ford administration...
Man: We're just waiting for our table up at Melville's.
Norm: So you'll move?
Man: Look, there's lots of other stools.
Norm: (starting to show signs of distress) Um...look, uh...um...sounds kind of s-...I'm, I'm Norm.
Man: I'm Jeffrey, and this is Hillary.
Woman: Nice to meet you. What do you do, Norm?
Norm: I sit there.
Woman: Well...nice meeting you...
(Norm starts to cough and seems to have trouble breathing.)
Cliff: Look, uh...this is, this is...we're running out of time here, he's already two stages beyond anything I've seen before, so I... I think you better give him the stool.
Man: I'm... I'm sorry, we're sitting here.
(Norm suddenly seems to pass out and collapses to the floor. Everybody rushes over to see if he's okay, including the couple he'd been talking to...at which point he gets up and sits on his stool)
Satchel in Get Fuzzy gets unhappy when anyone uses his beanbag.
In a rare video game example, Catherine has the four main guys going the same bar (The Stray Sheep) every night and sitting at the same table. They even sit in the same spots at that table.
Done hilariously in the first part of the endgame in Mass Effect 3. The Illusive Man's response to finding Shepard sitting in his office, after the latter has just destroyed his entire base of operations?
Also, Courage the Cowardly Dog. Eustace always sits in his chair and in a few cartoons would refuse to get off it and would get mad at anyone who tried to sit in it. His catch phrase eventually became the trope name, "This is my chair."
Woody's "spot" on Andy's Bed in Toy Story, as it represented his status as Andy's Favorite Toy.
The Simpsons, especially in the episode where the carnies steal their house, but also lampshaded/parodied in various opening credits.
Homer: Marge, he's messing up my ass-groove! It took me years to get that groove right!
South Park: Any time the kids gather at Cartman's house to watch a TV show, one kid (usually Clyde) will be kicked out of "Cartman's seat".
An Animaniacs cartoon had the Warner siblings stopping to eat at an Italian restaurant. The booth they sit at however happens to be the private booth of a local mobster who tells them so. Thus the conflict commences.
The c-plot of Gravity Falls episode 'Deep End' has Stan and Gideon fighting over the best chair at the pool. To be fair, the chair is not only at equal distance from the rest rooms and snack bar, has just the right amount of sun and shade, but is also pointed away from where Old Man Mc Gucket lotions himself.