"OK, you beat the game, now turn off your computer and do something constructive.
Like play racquetball.
or wash your car,
or cook dinner,
or join a funk band,
or travel to a foreign country
or run for president
or talk to a member of the opposite sex
or lube your car
or host a weenie roast
or dig for buried treasure
or milk a cow
or have a yelling contest with your neighbors dog
or perform brain surgery
or paint a yellow line in the center of your driveway
or write your name in the snow
or teach basket weaving to clams
or sing Welsh folk songs at the bank
or plant trees on public property
or confuse the person next to you
or make a triangular table
or ride a train
or arrange sock drawer alphabetically
or go bowling with your mom
or train potato bugs to do tricks
or make a quilt
or publish a magazine about pencil shavings
or eat lime jello with pineapple in it
or pave a freeway
or learn to draw
or take up photography
or learn to tell time
or photocopy money
or go out for pasta
or sew a dress
or bathe your iguana
or go fishing
or paint a stranger's house in the middle of the night
or take up windsurfing
or change your hair style
or sharpen whiteboard markers
or feed a toucan
or enjoy the sun
or do a crossword puzzle
or buy some cool clothes
or go to the beach
or play croquet with your dad
or water your plants
or build a doll house
or invite some friends over friends over for salmon and white wine,
NOT!
or play racquet ball,
or wash your car
…"

-MI2

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.