In-Universe Camera

In most movies, shows, video games, etc., the camera is assumed to not be actually present; one might say it exists outside the Fourth Wall.

An In-Universe Camera, as the name suggests, is actually present in the "world" of the story: Characters may notice and talk to it, it may get bumped or shaken by the environment, and may even be seen in a reflection. This frequently makes it a target for Camera Abuse, and works rather well with a Jittercam.

It's also a favorite device of the Documentary Episode, where another character is assigned a role of operating the camera. May lead to a Left It In situation, if a character explicitly asks for something to be "edited out" (but it's, of course, left in, since you the viewer are watching it).

When the camera is meant to represent the "eyes" of a character, it's a POV Cam.

See also Show Within a Show. For a gameplay mechanic that frequently uses this trope, see First-Person Snapshooter.

Examples of In-Universe Camera include:

Anime

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Yu Yu Hakusho is revealed to be composed of the case footage from Yusuke's time as a spirit detective. Considering some of the things we're shown throughout the series, including internal monologues, flashbacks, everyone's life before Yusuke even died, musical scores, and multiple camera angles, this footage must have been put through a lot of pre- and post-production.

Film

Surf's Up
The Blair Witch Project is a famous example, and almost epitomizes the trope.
Cloverfield
REC, its sequels, and the American remake Quarantine
Cannibal Holocaust
All of $la$her$ was shot from the view of a single cameraman on a murder game show. The camera was a character, one who followed the action for the studio and broadcast audience, but couldn't be harmed due to electrical collars on all the contestants and slashers.
The film 84 Charlie MoPic is explained in-world as the contents of a can of undeveloped film that came back from an LRRP (Long Range Recon Patrol) mission that had a combat cameraman attached.
Diary of the Dead
Paranormal Activity, its sequel, and the straight-to-video Asylum ripoff, Paranormal Entity.
Indie art film Guy is told entirely from the perspective of an unnamed filmmaker's camera as she documents the day-to-day life of a total stranger.
Rent uses this as a framing device, complete with its camera man, Mark Cohen.
The Truman Show has scenes that demonstrate the number and variety of hidden cameras capturing Truman's life.
The Troll Hunter.
Chronicle is shot through multiple in universe cameras. Most of it is from a camera owned by Andrew, a main character who almost obsessively documents his life, but it also includes the camera of Casey, a video blogger. In the last part of the movie, it switches between many different cameras, including security cameras, cable news, police video, and even camera phones.
There's a scene in The Tall Blond Man with One Black Shoe where the title character, an innocuous concert violinist, is identified as a spy in an airport. He walks through the concourse, putting a big piece of sticky candy in his mouth, and every few seconds the frame freezes, as various spies take his picture...always catching him with an awkward twisted expression as the candy gets stuck in his teeth.
The indie film Killer Flick, in which the main characters are a quartet of filmmakers who exist within the fictional world of the exploitation film that they are creating. The cameraman "One Eye" is usually shooting the footage that we see, but sometimes he appears in frame as well.

Live-Action TV

Mystery Science Theater 3000: The camera is an actual robot, "Cambot", and we see the show through his perspective. We only see him in the opening "Robot Roll Call", and he's actually looking into a mirror to show himself. That's why his name is backwards.
The Outer Limits episode "Manifest Destiny" was filmed almost entirely from this point of view.
The Sanctuary episode "Instinct": The first-person camera is held by the cameraman of the reporter who gets tangled up with the Sanctuary team while they're pursuing a giant insect.
The camera used by the documentary crew in The Office.
- The show seldom explicitly refers to the presence of cameramen, though. So seldom, in fact, that when the camera crew is actually discussed or referred to onscreen, it can be a little jarring.
The kinos in Stargate Universe are floating, remote control camera balls. They frequently are the camera for parts of most episodes and are the only cameras in the kino webisodes, as the name might suggest.
The Supernatural episode "Ghostfacers" was seen almost entirely through the lens of a few cheap cameras, carried by the Ghostfacers themselves.
Arrested Development is on the fence. While it's never explicitly stated to be a mockumentary, the camera acts like it's a person carrying a camera- it jumps, shudders, looks through keyholes and under doors. It also gets thrown out of a court in accordance with rules banning televised trials. So while it doesn't say so, it does this quite a lot.

Video Games

Halo: Combat Evolved has a scene shot from the perspective of a soldier's helmet camera, when they discover the Flood.
In Super Mario 64, the camera is actually controlled by a Lakitu member of a news crew following Mario around the castle. Being one of the first 3D platformers ever, and a very early example of a controllable camera, this functions more as an excuse to explain what a third person camera is than Lakitu actually being a proper character.
In the first Resident Evil, there's a scene from a S.T.A.R.S. member's shoulder camera before he gets devoured.
The basic mechanic of Suda 51's Michigan: Report From Hell is that the player is a cameraman, attempting to film the events that unfold. The story progresses differently depending on what the player films, including the option of ignoring the supernatural events to get pictures of the reporter's boobs and Panty Shots.

Web Original

Lonelygirl15
Kate Modern loves this, as characters frequently kick or drop the camera.
In Pure Pwnage, the camera is being controlled by Kyle, a character in his own right, with some notable exceptions for dramatic effect.
"The Sky Young Skit Show" is a rather humorous example of this. The skits are about three friends hanging around in L.A., in which one is never shown or named, as he is the designated cameraman, leading the titular character to say in a recent episode: "What are you? You're just like, a camera...and a hand...And why are you following me?" The interesting part about it is that in previous episodes, the characters interact as if the camera is not even there, causing the whole episode "Sky Discusses Faces" to get REALLY confusing.
Billy's webcam in Dr. Horrible's Sing-Along Blog serves as the camera during the blog segments of the episodes.
Anything to do with The Slender Man Mythos on youtube. Marble Hornets started it all, followed by Tribe Twelve , Everyman HYBRID and others.
The Joker Blogs: The first few entries consist of the title character's recorded therapy sessions with Dr Harleen Quinzel. After he escapes, he steals Dr Arkham's camera so he can keep making entries, and later uses Jack Ryder's.
Although the point of a vlog is to address the audience through the camera, Tobuscus takes it a step further by addressing the camera as the audience and introing every entry by asking the audience what they are doing in whatever ridiculous place he chooses.

"Audience? What are you doing in front of a steamroller, audience? That's precarious!"

Western Animation

The episode "Wild Cards" of Justice League, where the Joker set these up all over Las Vegas—along with twenty-six bombs. They played it pretty loose just to keep things going, though.
Sometimes invoked in Birdz, what with lead character Eddie sometimes filming his family in his aspirations to become a filmmaker.