Blair Witch Project/Cloverfield

The Blair Witch Project and Cloverfield differ from the standard shooting style in several different ways.

The whole film is presented as if it were an unedited documentary, filmed by the protagonists, and as such the shooting style resembles that of an amateur documentary or a home movie.
This includes shaking shots when the characters are running and more or less useless or irrelevant shots when the characters are just fooling around with the cameras.
A large part of the Blair Witch Project is in black and white, as one of the cameras that the protagonists carry with them only shoots in this format. This adds to the realism of the movie.

Ken Loach

The films of Ken Loach have an incredible authenticity and 'realness' to them. How does he achieve this?

Taken from "Loach on Loach"

Never use ADR
Run the entire scene for every shot, don't break the scene down into little "shot length" segments.
Light the entire scene so you're not artificially telling the audience "THIS is the lead actor for this scene, the others are less important"
Don't give the actors marks (indeed, you don't have to because you're lighting the entire scene)
Actors should have vulnerabilities

Dogme/Dogma

From Bright Lights Film Journal: Copyrights lawyers are out of luck. Anyone can obtain a Dogme certificate if [they] shoot a film in accordance with the ten rules known as "The Vow of Chastity."

The Vow of Chastity

Shooting on location (no imported props or sets)
Sound and image produced together
A handheld camera
Natural light
No optical work or filters
No superficial action (murders, weapons)
No temporal or geographic alienation
No genre films
Film format must be Academy 35mm.
No signature; the director must not be credited.

Alfred Hitchcock

A man dedicated to suspense and intrigue

Emotion is the ultimate goal of each of his shots. Hitchcock believed that emotion came directly from the actor's eyes. By bringing us closer or tearing us away he used camera angles to jerk us into the feeling of his moments.

The camera should be just like a person looking around for something out of place in a room. This allows the audience to feel like they are involved the action. Scenes can often begin by panning a room showing close-ups of objects that explain plot elements.

Hitchcock also loved to keep us on our toes by throwing in shots fast and close after being slow and far...

Sources

Bright Lights Film Journal - An article about Dogme films
IMDB Glossary letter: D - Dogme 95 explanation