Fake Video Camera View

There is a practice in some TV shows and especially in commercials that shows the view of someone using a video camera. This includes a rectangular "frame" in the scene, and the "REC" indicator with a red dot at the bottom right corner of the screen.

This is not the same as captured video, which includes the date and time stamp, but rather implies that we are seeing the video display on the camera from the viewpoint of the person recording it.

Examples of Fake Video Camera View include:

Anime and Manga

Suzumiya Haruhi: In the entirety of The Adventures of Asahina Mikuru, the Brigade's film project.

Film

In EDtv, several scenes are shown from the view of a professional video camera, complete with internal indicators and battery life, and filmed by main character Ed Pekurny and his cameraman.
Groundhog Day when Phil is filming the groundhog ceremony.
Tommy Boy: Richard is filming parts of the wedding.

Live Action TV

Good Luck Charlie: Used for Teddy's video diaries.
ICarly: Always used when Freddie is recording "live" segments of the web show. Mostly done to avoid Stylistic Suck by showing it 'as streamed' online.
The US home makeover show Trading Spaces had the Paige Cam (previously the Alex Cam), for episodes which featured an actual host. The footage was from a handheld camera carried by the host, but the footage was overlaid with the typical trappings of this trope, as well as the words "PAIGE CAM" (or "ALEX CAM").
Buffy the Vampire Slayer: In the episode "Storyteller" sometimes we see the red "REC" with the frame, when Andrew is recording something. Other times they show a green "PLAY" when he's reviewing video he shot earlier.

Video Games

Final Fantasy VIII: during the ending sequence.
Voyeur does this when the player is supposed to be recording footage.

Web Animation

The fourth episode of The Strangerhood mini-series "The Pitch" was done like this, as Sam's interaction with the focus group was being recorded for a "documentary style reality show sitcom".
Homestar Runner: A number of examples, including the "videos" on the character page and Strong Bad's "most amazing e-mail" from "Weclome [sic] Back".

Western Animation

Despicable Me: At the end. Notable in that they actually used a 1920x1080 resolution marker in the bottom corner.
Ed, Edd 'n' Eddy: One episode was almost entirely from the viewpoint of a camera. First there was a scene to set it up, then the rest of the episode is all the camera's view.