Doom Depot - Doom Music

PSX Doom, PSX Final Doom, Saturn Doom and Doom 64

These soundtracks have been officially released by Aubrey Hodges on his website. Here are the links to their respective pages:

Playstation Doom
Playstation Final Doom
Doom 64

Of note, the Saturn soundtrack is essentially the PSX soundtrack.
Additionally these have also been released on iTunes.

SNES Doom (Awesome Quality! by Elbryan42)

SNES Doom Intro Music	SNES Doom Intermission Music
E1M1 - At Doom's Gate	E2M3 - They're Going to Get You
E1M2 - The Imp's Song	E2M4 - Sinister
E1M3 - Dark Halls	E2M5 - Nobody Told Me About ID
E1M4 - Kitchen Ace (and Taking Names)	E3M1 - Untitled
E1M5 - Suspense	E3M2 - Donna to the Rescue
E1M6 - Demons on the Prey	E3M3 - On the Hunt
E1M7 - Sign of Evil	E3M6 - Waltz of the Demons
E1M8 - Hiding the Secrets	E3M7 - Facing the Spider
E2M2 - The Demons from Adrian's Pen

GBA Doom 1 & 2 (Awesome Quality! by Elbryan42)

GBA Doom	GBA Doom 2
E1M1 - The Imp's Song	Title Screen
E1M2 - Dark Halls	Intermission Screen
E1M3 - Kitchen Ace (and Taking Names)	Story Screen
E1M4 - Suspense	Map01 - Running from Evil
E1M5 - On the Hunt	Map02 - The Healer Stalks
E1M6 - Demons on the Prey	Map03 - Countdown to Death
E1M7 - Sign of Evil	Map04 - Into Sandy's City
E1M8 - I Sawed the Demons	Map05 - Doom
E1M9 - At Doom's Gate	Map06 - In the Dark
E2M1 - The Demons from Adrian's Pen	Map07 - Shawn's Got the Shotgun
E2M2 - Intermission from Doom	Map08 - The Dave D Taylor Blues
E2M3 - They're Going to Get You	Map10 - The Demon's Dead
E2M5 - Sinister	Map19 - Waiting for Romero to Play
E2M6 - Waltz of the Demons	Map21 - Message of the Archvile
E2M7 - Nobody Told Me About id	Map24 - Bye Bye American Pie
E2M8 - Untitled	Map27 - Adrian's Asleep
E3M1 - Donna to the Rescue	Map32 - Opening to Hell
E3M2 - Deep in the Code	Map33 - Evil Incarnate
E3M7 - Facing the Spider	Map34 - The Ultimate Challenge

GBADoomMIDIs.zip - Midi versions of the GBA tracks (made by Whitetiger)

32X Doom (Awesome Quality! by Elbryan42)

Map01 - At Doom's Gate	Map06 - On the Hunt
Map02 - The Imp's Song	Map07 - Demons on the Prey
Map03 - Dark Halls	Map08 - Sign of Evil
Map04 - Kitchen Ace (and Taking Names)	Map09 - Hiding the Secrets
Map05 - Suspense	Credits - Bunny
Stats Screen - Intermission from Doom

3D0 Doom (ripped by cybdmn)

E1M1 - At Dooms Gate	E1M5 - Suspense	E1M9 - Hiding the Secrets
E1M2 - The Imps Song	E1M6 - On the Hunt	E2M1 - I Sawed the Demons
E1M3 - Dark Halls	E1M7 - Demons on the Prey	E3M1 - Untitled
E1M4 - Kitchen Ace	E1M8 - Sign of Evil	E3M2 - Donna to the Rescue

Jaguar Doom

Title Music	I Sawed The Demons	Nobody Told Me About id
The Imp's Song	The Demons From Adrian's Pen	Donna To The Rescue
Kitchen Ace (and Taking Names)	Intermission From DOOM	At Doom's Gate
On The Hunt	Sinister

Ultimate Doom & Doom 2 MP2s (from Doomworld)

Ultimate Doom	Doom 2
Ultimate Doom - Title Music	Doom 2 Title Music
Ultimate Doom - Victory Music	Doom 2 Intermission Music
Ultimate Doom - Endgame	Doom 2 Endgame
E1M1 - At Doom's Gate	Map01 - Running from Evil
E1M2 - The Imp's Song	Map02 - The Healer Stalks
E1M3 - Dark Halls	Map03 - Countdown to Death
E1M4 - Kitchen Ace (and Taking Names)	Map04 - Between Levels
E1M5 - Suspense	Map05 - DOOM
E1M6 - On the Hunt	Map06 - In the Dark
E1M7 - Demons on the Prey	Map07 - Shawn's Got the Shotgun
E1M8 - Sign of Evil	Map08 - The Dave D Taylor Blues
E1M9 - Hiding the Secrets	Map09 - Into Sandy's City
E2M1 - I Sawed the Demons	Map10 - The Demon's Dead
E2M2 - The Demons from Adrian's Pen	Map18 - Waiting for Romero to Play
E2M3 - Intermission from DOOM	Map20 - Message of the Archvile
E2M4 - They're Going to Get You	Map23 - Bye Bye American Pie
E2M6 - Sinister	Map25 - Adrian's Asleep
E2M7 - Waltz of the Demons	Map28 - Getting Too Tense
E2M8 - Nobody Told Me About id	Map30 - Opening to Hell
E3M1 - Untitled	Map31 - Evil Incarnate
E3M2 - Donna to the Rescue	Map32 - The Ultimate Challenge
E3M3 - Deep into the Code
E3M8 - Facing the Spider

Doom 1 & Doom 2 Midis (contributed by BigBadGangsta)

Final Doom: TNT Evilution MP3s (by Bigbadgangsta)

Title Screen	Story Screen	Map02	Map05	Map07	Map10	Map14	Map20
Stats Screen	Map01	Map04	Map06	Map08	Map11	Map16	Map22

bigbadgangsta.txt - Readme file that came with the files.
Final Doom: TNT Evilution Midis (contributed by Elbryan42)