Recut: The Curse has the most stunning example of this. Apparently, the film ran over time and budget, so the suits decided to take it over to see how they could screw it up. Their version is the Theatrical Cut. When the film was shown on TV, someone got a hold of the now infamous Producer's Cut. While the violence and cursing were trimmed, an assload of alternate takes and different opening narration were shown, and the entire last 20 minutes of the film is RADICALLY different from the Theatrical Cut. The main change is that the explanation for Michael's killing ways is altered: The Theatrical version offered a scientific reason, but the Producer's Cut says the reason is supernatural (which also explains why Michael is also growing bigger in each previous film. It's because his power is growing). It also shows a final scene with Dr. Loomis realizing that he has been cursed by Thorn. This was likely altered when Donald Pleasance died. An early trailer showed that the film was originally going to called "Halloween 666: The Curse of Michael Myers." This version is only available through bootleg video releases.
What Could Have Been: Before the "Cult of Thorn" plot was fleshed out, the writers toyed with the idea of having the Man in Black be revealed to be Michael's father.
Donald Pleasence died during the shooting, so we never got to see his personal confrontation with Michael.
Not exactly true. The Producer's Cut of Halloween 6 was a finished version of the movie and the version producer Moustapha Akkad wanted to release (hence the name). Donald Pleasence successfully finished shooting of that film. It was only when the reshoots came about for what would become the Theatrical Cut that Pleasence had died.
Danielle Harris wanted to reprise her role as Jamie, but was turned down because they would've had to pay her more money.