Space Invaders definitely takes the cake for its interesting and wacky variations. The 16 different ways that the aliens can attack are cool, but all the different ways two players can cooperate are just downright insane. One player moves right, the other moves left? Any two people who actually dare to try that will either go on to be two of the world's best negotiators, or will kill each other inside five minutes.
Asteroids,
Pac-Man,
Missile Command and
Berzerk are worth mentioning because the version of each game most faithful to its arcade counterpart was not at variation #1. Once you discovered where the "fast" asteroids, the "smart" cruise missiles, the quick ghosts and Evil Otto were hiding, you had a better way to show off the skills you learned at the arcade.
The variations of
Haunted House do an excellent job of ramping up the game's difficulty, much like the different skill levels available in many games today. If you beat #1, try #2. Beat #2 and progress to #3... all the way up to #9. I've never beaten #9. Come to think of it, I don't think I ever mastered #8, either.
Finally,
Yars' Revenge may be the earliest game to offer essentially two completely different levels of complexity in the same game, kind of like how some racing games offer "arcade" and "simulator" modes today. There were the standard variations we know and love, but then there was variation #6 (#7 for two players), with more bits for the player to keep track of, from requiring a certain number of "TRONS" to activate the cannon, to flying back to the left side of the screen before actually being able to use the cannon. This variation was even given its own name in the manual, "Ultimate Yars."
Edited by FujiSkunk, Sun Jan 1, 2012 10:27 PM.