Separate Player's Body

The Separate Player's Body glitch is very easy to do. One variation glitch can only be done on Metropolis, Gravemind, Uprising, or The Great Journey; another variation can be done anywhere. If you shoot your legs, though, you will get hurt.

Metropolis or The Great Journey
When the Scarab stops moving, go onto one of the back legs, walk into the body of the scarab, move back a little, and look down, and you will see the lower half of your body separated from the rest.

Gravemind
Go into the Mausoleum of the Arbiter and kill all the enemies, or wait for them to kill each other. Then walk up to the Arbiter's armor sarcophagus and try to walk "inside." Look down, and you will see the lower half of your body separated from the rest.

Uprising
When you reach the level you will see a big hill you can jump to. When you're on the hill, go straight so you hit a mountain. Then, go right and you'll see a little path. Go on the path. Then, you will see the end of the path. Slowly go in it and look down, and you will see the lower half of your body separated from the rest.

Any level
Look down and turn in a circle very quickly. Your legs will not turn as fast as your torso, and will be separated briefly.

Why it happens
When Bungie modeled the characters in the game, they modeled the two halves separately to make it easier to animate turning without moving your legs. This results in some unintentional separation because of the shape of some of the game's geometry.