Yuki Kajiura (The Garden of Sinners)

Winifred Phillips (Speed Racer The Videogame)

Clint Mansell:
Requiem For A Dream
Death is the Road to Awe
An End, Once and For All

Damn, you were quick to take some great ones!

I can't comment on the entire breadth of their work for some of these, so it's a good idea you asked for examples:

- Basil Poledouris - Lights On (from Cherry 2000) | Klendathu Drop (from Starship Troopers)
- James Horner - Main Title/Takeoff (from The Rocketeer)
- Thomas Newman - That Next Place (from Meet Joe Black)
- Rachel Portman - Junuh Sees the Field (from The Legend of Bagger Vance)
- Daft Punk - Disc Wars (from Tron: Legacy)
- M83 - I'm Sending You Away (from Oblivion)
- Lorne Balfe - Tank Battle (from Ghost in the Shell) | Labored and Lost (from Assassin's Creed Revelations)

Since I've now entered game soundtracks, here are a few other composers:

- Austin Wintory - To Know, Water (from Abzû)
- Olivier Deriviere - Memory Reconstruction (from Remember Me)
- Solar Fields - Catalyst (from Mirror's Edge: Catalyst)
- Keiichi Okabe - Bipolar Nightmare (from Nier:Automata)
- Berlinist - Gris, Pt.1 (from GRIS)
- Joe Hisaishi - Happily Ever After (from Ni no Kuni II) | The Journey to the West (from Princess Mononoke)

And we now transition to anime, but this has gone on long enough, so I'll just name a couple:

- Evan Call - The Love That Binds Us (from Violet Evergarden)
- Jeremy Zuckerman - Greatest Change (from The Legend of Korra)

I agree.
I was glad to see Reznor get a lot of praise for his work on the Ken Burns "VIetnam" TV series.

I think this discussion was intended for music written specifically for a game, but has drifted into Music Not written for but used with a game. A lot of the Lucasarets Star Wars games just used music lifted directly from the film soundtracks.
But in that category I think the first two Bioshock games use of music from the 30 and 40's was brilliant. I single out "God Bless The Child" in the scene where, in "Bioshock" Jack wakes up in Brigit Tannenbuam's apartment with the Little Sisters.....

If you enjoy the music from Metroid, Metroid - Harmony of a Hunter-101% Full Album is a must. I leave it on while I do stuff more often than I'm willing to confess.

On a related note, I'd like to tie up and throw lawn darts at whoever composed the Super Mario Bros theme. :P

In no particular order:

Bernard Herrmann
The Day the Earth Stood Still
Vertigo
Psycho
Jason and the Argonauts
Cape Fear
Taxi Driver

Bebe and Louis Barron
Forbidden Planet

Popol Vuh
Aguirre, the Wrath of God
Heart of Glass
Nosferatu the Vampyre

Tangerine Dream
Sorcerer
Thief
Firestarter

Goblin
Profondo Rosso
Suspiria
Tenebre

Klaus Doldinger
Das Boot
The Neverending Story
Salt on our Skin

John Carpenter
Assault on Precinct 13
Halloween
Escape from New York

Angelo Badalamenti
Blue Velvet
Twin Peaks: Fire Walk with Me
Mulholland Drive

Paul Haslinger
Underworld

Don Davis
The Matrix

Henry Mancini
Experiment in Terror
The Pink Panther
Charade
Gunn
The Party
Lifeforce

Harold Faltermeyer
Beverly Hills Cop
Top Gun
The Running Man

Giorgio Moroder
Midnight Express
Cat People
Scarface

Fabio Frizzi
Contraband
City of the Living Dead
The Beyond

Akira Ifukube
Gojira

Thom Yorke
Suspiria [2018]

Ryuichi Sakamoto
Merry Christmas, Mr. Lawrence
The Last Emperor
The Revenant

Éric Serra
Leon: The Professional
The Fifth Element
GoldenEye

Nino Rota
The Godfather

Kenji Kawai
Ghost in The Shell

Danny Elfman
Batman
Sleepy Hollow
Spider-Man

Lalo Schifrin
Bullitt
Dirty Harry
Enter the Dragon

Brad Fiedel
The Terminator
True Lies
Johnny Mnemonic

Soyo Oka, composer for Sim City (SNES), Super Mario Kart, Pilotwings and other delightful projects.

Hiroki Kikuta, legendary composer all around, but what I remember them for is the Mana series.

The Follin Bros, composers of many games of the west, including the best Pictonary theme you've ever heard.

Some great choices, I think we share similar tastes :) I could also easily have added Basil Poledouris - Conan the Barbarian, Jerry Goldsmith - The 13th Warrior and James Horner - Gift of a thistle to my list.

As for anime, I wouldn't be able to identify a favorite composer. At best a couple of favorite songs, like the intro to Blue Gender.
The music from The Edge is great as well, it's just a pity that the film's got such a (to me at least) nonsensical ending, otherwise it would've been a firm favorite.

As for the other mentions, I'll have to take my time and go through them one by one thank you.
The infinity engine games have some great pieces of music, and Planescape may very well have the best. Case and point. Though personally I might put IWD 2 ahead of, e.g. Skeleton of a Town with Jeremy Soule I think

Not something I've paid that much attention to in films but I guess Danny Elfman.

For games I've made an 80s top list on my site, will probably do 90s and beyond eventually as well as flesh this one out a bit with text:
https://minirevver.weebly.com/top-composers-1980s.html

Limiting to games. A couple names I want to share because they're not as often recognized as the "big ones" like Soule, Uematsu, Uelmen, etc. I'll refrain from listing some of the greats as others are covering it.

Frank Klepacki (Command and Conquer, most other Westwood titles, others)
Jeehun Hwang (Mechwarrior 2, Dark Reign, others)
Ben Prunty (FTL, others)
Eric Barone (Stardew Valley)
Rich Vreeland (Mini Metro)

A big reason I only went to games: game music and film music are often quite different in important, meaningful ways.

Jeremy Soule (Star Wars KotOR) - it's almost as if John Williams did it

From the 8-bit C64 era:

Rob Hubbard
Monty On the Run: https://www.youtube.com/watch?v=4EcgruWlXnQ

Martin Galway
Comic Bakery: https://www.youtube.com/watch?v=nf29ShkoAiA

Ben Daglish
The Last Ninja: https://www.youtube.com/watch?v=1ok1ChTtWQI

A couple film composers (not to say that's all they've done, however):

Daniel Pemberton - The Man from U.N.C.L.E. (itself being a much better film than most gave it credit for), Spider-Man: Into the Spider-Verse, etc.

Joseph Bishara - Insidious, The Conjuring... numerous other films in that "cinematic universe" in addition to him even appearing in them as certain demons