Video Collage

A Video Collage is a video made from clips of video and animation, juxtaposed in various ways. While video collages have existed as an art form since the 1960s, they were something of a film-school peculiarity until the explosion of video capture and editing tools and the rise of online video repositories such as YouTube made it a rather trivial matter to put one together.

Generally overlaps with the following, many of which use video collage extensively:

Animutation (basically a sub-trope)
Fan Vid
Stupid Statement Dance Mix (the accompanying videos are typically done this way)
YouTube Poop

The Other Wiki calls this a "Collage film".

Examples of Video Collage include:

Precious Images, an eight-minute film from 1986 made by Chuck Workman, composed of about 470 half-second-long moments from films through the history of cinema, from 1903's The Great Train Robbery to Rocky IV (1985). Films of virtually every genre are represented, and in some cases are organized by genre, with appropriate musical backing. The film was commissioned by the Directors Guild for its 50th anniversary, and won the 1987 Academy Award for Live Action Short Film. It was reissued in 1996 with new clips from films made since its original release, and in 2009 selected for preservation in the United States National Film Registry.
Dead Men Don't Wear Plaid, a 1982 Film Noir parody starring Steve Martin, incorporates clips from nineteen vintage films with new footage shot in black-and-white to create a completely new story incorporating the dialogue and action from the period films.
The 1973 animated short Frank Film made by Frank and Caroline Mouris is a nine-minute compilation of images cut from magazines interwoven with two different narrations. It won the 1974 Academy Award for Best Animated Short Film and was inducted into the National Film Registry in 1996.
The work of rogue filmmaker Mike Jittlov often blends collage and Pixilation to produce his signature style.
The Documentary Los Angeles Plays Itself, a video essay exploring the portrayal of the city of Los Angeles in film. Clocking in at nearly three hours in length, it consists almost exclusively of clips from other films with narration. In addition to examining the early history of Los Angeles in film, often as California Doubling for other cities, it also highlighted now-gone immigrant enclaves displaced and destroyed by skyscraper construction in the 1960s and 70s. Although it was completed in 2003, it wasn't commercially released for another eleven years.