Jay Doubleyou: the mockumentary

One form of documentary is the form that 'mocks' or 'makes fun of' the format:
Mockumentary - Wikipedia, the free encyclopedia
20 Best Mockumentaries | TotalFilm.com

It started like this perhaps:

BBC: Spaghetti-Harvest in Ticino - YouTube
Panorama - April Fool's Day Hoax - Spaghetti Harvest - 1st April 1957 - YouTube
Spaghetti-tree hoax - Wikipedia, the free encyclopedia

A more modern example of a 'short':

The Majestic Plastic Bag - A Mockumentary - YouTube

Some would describe this as a 'mockumentary':

A Hard Day's Night (The Beatles) Película Completa Subtitulada al Español - YouTube

A Hard Day's Night (1964), written by Alun Owen, and purporting to describe several days in the lives of The Beatles, was possibly the first feature film that could be characterized as a "mockumentary".
Mockumentary - Wikipedia, the free encyclopedia

Or you might prefer this:

The Rutles - All You Need Is Cash - YouTube

The film has many cameo appearances by both British and American comedians, including Monty Python, Saturday Night Live andRutland Weekend Television. George Harrison has a cameo role as a television journalist conducting an interview outside the headquarters of Rutle Corps, oblivious to the stream of people coming out of the building carrying items stolen from the office; this is a reference to the Beatles' famously plundered Apple Boutique and Apple Headquarters, where even the ceiling lining was looted. The interview ends abruptly as the microphone is stolen out of his hand.
All You Need Is Cash - Wikipedia, the free encyclopedia

Talking of music, some would say this is the best:

This Is Spinal Tap - Trailer - HQ - YouTube
This Is Spinal Tap - Wikipedia, the free encyclopedia
This Is Spinal Tap - Rotten Tomatoes
Spinal Tap Fan Site and This is Spinal Tap

Then we have a little more music:

Borat - Wikipedia, the free encyclopedia

Borat - Throw A Jew Down The Well and others - YouTube

However, this is considered the modern grandaddy of the mockumentary:

The Office - My Top 25 Funniest Lines - YouTube

When it was first shown on BBC Two, it was nearly cancelled due to low ratings, but has since become one of the most successful of all British comedy exports.
The Office (UK TV series) - Wikipedia, the free encyclopedia

But a recent favourite has to be this look at the lead-up to the London Olympics: