The closeup of the dog on the back of the MI1 box never showed up in the actual game, due to restrictions on disk space.
Herman Toothrot was not originally written for the game, he was added when testing revealed how boring the island was with just the cannibles to talk to.
In an interview with Computer Gaming World, Steve Purcell discussed a puzzle that was cut out of MI1 for disk space reasons. He said that at one point during the endgame, Guybrush would have been on a dock surrounded by a group of ghosts. To get out of the situation, he needed to use the head of the navigator as a bowling ball and knock the ghosts over.
However, it might not have been the head of the navigator, but the cannonball from Herman Toothrot's fort. It makes sense: the object has no use in the finished game, making it likely that its point of use was cut out, and when Guybrush looks at the cannonball he observes that it "has three holes in it," just like a bowling ball!
As an aside, Tim Schafer liked the puzzle enough to reuse it in Day of the Tentacle.
The giant monkey robot idea from MI4 was originally planned for MI1, with LeChuck's ghost ship (transformed in a power rangers/transformers manner) as the robot's opponent, but the idea was thrown out early on for being too weird. It was then revived for MI4 when they couldn't think of anything better.
They originally planned on, not only reviving insult swordfighting for MI2, they were going to have different insults for all three islands.