Psycho: influences, sequels,
remake, homages
Influences on Psycho:

Ed Gein & Robert Bloch's novel Psycho
Jack the Ripper, Dr. Crippen, & Christie

Expressionism:
in art
in film:
The Cabinet of Dr. Caligari (1920), directed by Robert Wiene
The Last Laugh (1924), directed by F. W. Murnau
M (1931), directed by Fritz Lang

Soviet montage theory:
Montage theory developed by Eisenstein and Vertov

Influences: works by contemporary directors:
Les Diaboliques (1955), directed by Henri-Georges Clouzot
The Night of the Hunter (1955), directed by Charles Laughton
Touch of Evil (1958), directed by Orson Welles
Macabre (1958), directed by William Castle

Psycho sequels:
Psycho II (1983), directed by Richard Franklin
Psycho III (1986) directed by Anthony Perkins
Psycho IV: the Beginning (1990), directed by Mick Garris

Psycho remake:
Psycho (1998), directed by Gus Van Sant

Other films based on or influenced by the Ed Gein story:
Deranged (1974), directed by Jeff Gillen & Alan Ormsby
Ed Gein, aka In the Light of the Moon (2000), directed by Chuck Parello
Silence of the Lambs (1991), directed by Jonathan Demme
The whole sub-genre of slasher movies, including the Nightmare on Elm Street series, the Halloween series, the Friday the 13th series, and the Scream series

Homages to Psycho and Hitchcock (among many):
Dressed to Kill (1980), directed by Brian DePalma
High Anxiety (1977), directed by Mel Brooks
24 Hour Psycho (1993), by Douglas Gordon
The Simpsons, especially the episodes Itchy & Scratchy & Marge in season 2 (parody of the shower scene) and Black Widower in season 3 (parody of the fruit cellar scene)