E1M1 - At DooM's Gate = Metallica - Master of Puppets/No Remorse
E1M4 - Kitchen Ace(And taking Names) = Pantera - Rise
E2M1 - I Sawed The Demons = AC/DC - Big Gun
E2M2 - The Demons From Adrian's Pen = Metallica - The Call of Ktulu
E2M3/Intermisson Music - Intermission From DOOM = Pantera - Regular People
E2M9/E3M1 - Untitled = Pantera - Mouth of War
E3M3 - Deep Into the Code = Slayer - Behind the Crooked Cross
E3M8 - Facing the Spider = S.O.D - Sargent D And The SOD
Map01 - Running From Evil = Megadeath - Hangar 18
Map07 - Shawn's Got the Shotgun = Slayer - South of Heaven
Map10 - The Demon's Dead = Black Sabbath - After All (The Dead)
Map18 - Waiting for Romero to Play = Pantera - This Love
Map23 - Bye Bye American Pie = Alice in Chains - Them Bones
Map25 - Adrian's Sleep = Alice in Chains - Angry Chair
Map31 - Evil Incarnate = Wolfenstien 3D (Game)
Map32 - The Ultimate Challenge/The Ultimate Conquest = Wolfenstein 3D (Game)

Props to "blood imp" from the http://www.newdoom.com forum