Floating plasma grenade
From Halopedia, the Halo wiki
Assault on the Control Room
On Assault on the Control Room, when you get to the first lift, stand behind the sign that says "Press X to activate lift" and throw a plasma grenade into the center of the lift. The lift will go down, but the grenade will float in front of you. The grenade will harm you, so you will die after it explodes if you have low health.
Pillar of Autumn
On Pillar of Autumn, after Captain Keyes gives you the pistol, kill the Grunts and return to the bridge. Kill one of the crewmen or Captain Keyes, and the invincible Marines will enter the bridge. Let them attack you until you have low health, and throw a plasma grenade when -- not before—you die. The grenade shouldn't leave your hand when you die; it will float in the air for a while and explode.
You need two players, one with a rocket launcher (Person A) and one with plasma grenades (Person B). Have Person A stand still and look straight ahead, and have Person B throw a plasma grenade onto the tip of the rocket launcher. Once the grenade stops moving, have Person A back off. The grenade will float until it explodes.
These instances of the glitch all have the same cause. When a plasma grenade sticks to an inanimate object, such as a wall or a weapon, the game stops calculating physics for the object—this is done under the assumption that the inanimate object will not be moved. The problem happens when a grenade is stuck to an inanimate object that does move, such as the floor of an elevator or the tip of a held weapon. When the object moves, the grenade does not move with it, because the game does not synchronize the two items' movements.