Setting as a Character

In most works, the setting is static. A backdrop against which the world itself is painted. The world affects the characters, but it doesn't interact with them. These works are different. Sometimes the setting itself is a character in the work. It interacts with the characters. Reacts to what they do. It's almost like the setting understands the characters, and is one itself.

This is most likely when the setting is some kind of ship. Spaceships and large boats are good for breaking down at inopportune moments, then starting right back up after the mechanic sweet talks them. Any sort of setting that functions as a character in the narrative works though.

Note: This is NOT Genius Loci, a location that actually is a living being. The landscape isn't actually alive, it just acts like it at times. When the setting is a space ship, don't confuse it with Sapient Ship (a ship that thinks and talks) or a Living Ship (an example of Organic Technology).

Examples of Setting as a Character include:

Anime and Manga

Vandread: the Nirvana (or more accurately its power source, the Paksis) is alive, but communicates more through feelings rather than words.
Space Battleship Yamato: the Yamato is the main character of the show. It is the ship's fighting spirit that enables their amazing victories.
One Piece: the Merry Go is was considered a character. It has been featured on the title page (a spot reserved for the Straw Hat Crew), crew members have caught brief glimpses of a shadowy spirit-like figure fixing it(self), and, at one point, came seemingly out of nowhere to pick the crew up. It even had some last words to say to the crew just before it died.

Comic Books

Sin City is the main character of the series according to Word of God. The protagonists refer to the city as a living being metaphorically, mentioning how she thinks and acts. The city is also said to have a negative effect on peoples' state of mind.
Astro City is the happier version of the above example. The city inspired much more hope and awe, mostly due to being a City of Adventure.

Film

Event Horizon: the eponymous spaceship went To Hell and Back and has become an Eldritch Location. Though it doesn't appear sentient, it seems to act as a malevolent force.

Music

The Protomen, refer to The City as a character, in both Act I and Act II. A city that's asleep and in darkness but that will be woken up. It doesn't wake up though.

Literature

Discworld: where a (sailing) ship has proved 'alive' enough to have an actual post-death existence.
- Ankh-Morpork would definitely count as well, especially in the Night Watch books. Various characters have described the city as a Brilliant but Lazy Loveable Rogue, who is utterly filthy, hates royalty, and shies away from conflict so it can defeat enemies via either bribery or assimilation.
Codex Alera: Captain Demos' ship The Slive is one giant wood fury; as such, Demos is able to manipulate it to give himself an advantage in nearly any fight that occurs on it.
China Mieville uses this trope frequently, and very well. Perdido Street Station, Kraken, and The City and The City are all good examples.

Live Action TV

Firefly: Played with in the final episode when River tricks the bounty hunter Jubal Early into believing that Serenity, the ship which is constantly anthropomorphised throughout the series, is actually alive, and that she has become a part of it.
- The metaphorical meaning also applies - Whedon considered the ship to count as a main character (just ahead of River's feet).
Stargate Universe: Destiny, the Ancient ship that's home to the main characters. While it's not actually sentient (we think), it had enough quirks and foibles to fall into the category within the first few episodes. For the first season, the ship navigates on its own and runs 90% of functions without the crew's input, based on parameters set by the Ancients that the main characters can't figure out. In season 2, we learn that the ship can affect brain waves to cause dreams and hallucinations.
Star Trek: The Original Series: USS Enterprise, NCC-1701, was a big part of Engineer Scott's appeal as well; he served as her advocate amongst the cast and was most directly responsible for her life-saving bursts of energy.

Western Animation

Biker Mice From Mars: A variation on this trope, though never expanded upon: the bikes are alive, and have feelings. When neglected, they buck their riders and sulk. Lil' Hoss (Modo's bike, the only named bike on the show) has the most AI.

Video Games

Silent Hill: "Silent Hill" seems to have a personality, doubled by the fact that it bases its forms by the heart of those that enter.