I'm a fan of the original DOOM games, I've already beaten the first one 3 times, and for my 4th time, I thought I'd try playing with only the mouse.
Here are the controls :
Move Forwards/Backwards - Move the mouse vertically
Pitch Camera - Move the mouse horizontally
Strafe - Move the mouse horizontally while holding Mouse2 Fire - Mouse1
Interact - Double click Mouse2 / Press Mouse3
Cycle Weapons - Mouse Wheel

(Game is being run in Chocolate DOOM 3.0.1 running The Ultimate DOOM as an IWAD with a custom PWAD replacing Doomguy's mugshot with me you can download once I make a link)