I've got two from the original Halo that I can think of at the moment.
The first was on the level Silent Cartographer, during the part where you are going through the underground base. Anyhow, as a buddy and I were backtracking through the base to get back outside we came into a room that was suppose to be empty but instead had an Elite floating in the air for some reason, in a standing position. When we came into the room he made the sound signifying you've been seen, but didn't move at all. When aimed at the reticules wouldn't turn red, and if you let go of the analog stick while looking at the Elite the reticule would start to drift away from him. Anyhow, when it came to shooting him blood would come out, but he had no shields and wouldn't die. We tried a few more things, and when we got bored we went to continue the level. However as we hit the loading zone on the way out there was an Elite dieing sound from the room we left. Sure enough on the way out we found him dead on the ground below where he was floating. Quite the mystery as to what caused that.
The second one takes place during the cinematic at the end of the Assault on the Control Room level. Now, we had decided to just run past the Hunters guarding the final door to see if anything different would happen. As chance would have it I got shot in the back and died just as the cinematic started. When it did it opened with my dead body lying right in front of the door. Then the camera panned away as an invisible Master Chief walked along the bridge thing that leads to the controls. I thought that nothing else would happen, but when Chief starts talking to Cortana my body had moved to lying where I was suppose to be standing. As they continued talking the body switched to a weird upright position, which essentially looked like he was standing in a slouch at an angle with all the leg below his knees stuck under the ground. The crowning moment of the whole thing was when the Chief exclaims "Keyes!" in a shocked voice and the camera zooming in on where I was suppose to be, which still had the Chief's weirdly angled head sticking into the shot.
Wow, those took a lot more explaining then I thought they would. I think I still have both of those videos on a VHS (I was very happy when I first figured out I could record my games that way) and I kinda wonder if there would be some way to upload them to my comp.