Immobile Banshee

The Immobile Banshee glitch is only available for Halo: Combat Evolved in the PC.

Walkthrough
First, grab a Banshee and place it near a Scorpion. Get out of the Banshee and ride the tank. Using the tank, push the Banshee so that one of it's Gravity Pods is stuck into a crevice on a wall. The tip of the Banshee's wing should get stuck into the cliff wall and the Banshee can hardly move, even if you try to flip it or throw grenades at it.

Another way to make an immobile banshee is to fly it over a wall, then dropping it so that it's opening will "bite" the wall.

Also, in the multiplayer level Blood Gulch, you can fly the Banshee and land it in a tree that is present at both bases. If done correctly, it will stick in the tree and explosions won't be able to dislodge it. It should shake the whole time and not respawn. The inability to respawn is probably due to the motion, as moving Banshees don't respawn at the base. Many people do this on purpose, as using a Banshee is considered unfair and "noobish" due to the imbalance of power.

Be careful though, playing with the immobile Banshee can be dangerous. When you try to flip it while you are near the wall, you might get squished.

It sounds impossible to do, but with a little luck and a lot of patience, it is possible.