Name some movie scores that are so famous that after hearing only a few seconds of the music, you can immediately name the movie.

Fight club.

Star Wars

Indiana Jones

Jaws

Back To The Future

The Exorcist

Beauty & The Beast

The Gremlins

Close encounters of the third kind.

The Inception "BRAAAAAAAAM".

Halloween

Rocky

Once upon a time in the west

The Magnificent Seven, Jaws, Mission: Impossible (I know it's originally from the TV series), Rocky, Gone With the Wind, The Godfather, Star Wars and the James Bond theme.

The Great Escape

Psycho.

Jurassic Park

Interstellar

Plenty of the scores already mentioned.

Oh, Bernard Herrman would be up there:

Psycho and North by Northwest.

Also, John Murphy's score for 28 Days Later has cropped up in various promos and ads over the years.

Michael Kamen did an excellent job on Brazil, but that might not be instantly recognisable for everyone.

Help! and A Hard Day’s Night.

Midnight Express

The Godfather

The Good the Bad and the Ugly

The Deer Hunter (although the music was originally written for another movie)

Mission Impossible, it's impossible to miss (pun intended)

Rocky

Good, Bad and Ugly

Demolition Man

James Bond Theme (and 'A View to a Kill' by DURAN DURAN)

2001: Space Oydssey

Star Wars

Godfather

Hard Day's Night

Yellow Submarine

Jaws

Mrs. Robinson (from 'The Graduate')

Police Academy

The Good the Bad and the Ugly has already been mentioned so

Easy Rider.

Apocalypse Now.

Pulp Fiction.

Mysterious Skin

Aguirre, Wrath of God

Saturday Night Fever

Requiem For A Dream

The Third Man

Not a score, but this:

https://www.youtube.com/watch?v=1c8Selr9Aec

The Vengeance Trilogy

Chungking Express

It's hard to name Japanese movie though, i wanted to name at least one but not easy to remember.

Pirates of the Carribeans

Superman

Forrest Gump

Harry potter

Lord of the rings

E.T

Ghost Busters

Amelie

PS : Cheated a bit