This is in part a response but also an expansion on the essay by Patrick Curry entitled 'Everything I know about game design I learned from Super Mario Bros.'
The paper dissects the 1985 game and reveals the secrets of game design held within.
One section I wish to address is a paragraph discussing what Curry refers to as a mini-game within Super Mario Bros. This is the flag pole at the end of every level. The player acheives a greater number of points the further up they can land on the flagpole, capping out at five thousand. Exceptional players can even jump the flagpole itself (a feat I have not been able to achive as of yet). This mini-game is an end of level reward in its own way. You've survived the challenges thrown at you, so now have some fun and try and jump over the flagpole. What amazed me about this approach to the level's end in Super Mario Bros upon further thought is that Shigeru Miyamoto has continued this pattern of end of level mini-games throughout the entire Mario series (granted some are more abstract than others, but we're going to analyze them anyway).
Let's start with the final two NES titles in the series. Super Mario Bros 2, and Super Mario Bros 3. SMB2 was a remake of the Japanese titled Doki Doki Panic, which used the Mario characters to increase game sales when it was ported to American shores. None the less the end of each level ended with a slot machine style game where the coins you collected could be exchanged for extra lives if the slots paid off. This took the mini-game concept a step further in that collecting coins throughout the level had more of a purpose (well ok, in SMB if you collect 100 coins you get a 1up. In SMB2, coins allow you to play a slot machine to recieve 1ups. It's not that different but it ties the coin-1up relationship into the end of the level). In SMB3 there is a single slot where powerups rotate through. Like SMB2, you need to get three of a kind to achieve 1ups (hence you only have a chance every three levels in this game). A mish-mash of powerups would still yield a 1up or two, but if you achieved three stars, you get a prestigious five 1ups, which was always a discussion point amongst friends about various strategies to net yourself a star at the end of a level.
The Game Boy Marioland games (and then the Warioland games) continued this tradition of the end of level mini-game in many interesting ways. However these were designed by Gumpei Yokoi (the creator of the Game Boy), and not Miyamoto, so I will acknowledge their continuation of this pattern and move on (the same with New Super Mario Bros on the DS, designed by Shigeyuki Asuke which returns the flagpole from SMB).
The SNES had two Mario games, both continuing the formula. Super Mario World's mini-game is reminiscent of the flagpole from SMB as each level ends with can only be described as a giant hurdle. The middle part rises and falls and the player gets a higher number the further up he can hit the hurdle. The number is saved and when the player plays enough levels to make one hundred a 1up mini-game is played. In Super Mario World 2: Yoshi's Island, each level has five flowers scattered around. When they are collected (which is part of getting a perfect score of 100 for each level), they are added to a roulette wheel at the end of the level that Yoshi jumps through. If the wheel lands on a flower, the player partakes in one of many mini-games for 1ups and powerups.
Now the 3D Mario games all share their level ends in common, and it's not what I can actually call a mini-game. In Super Mario 64, Super Mario Sunshine and Super Mario Galaxy, the purpose of each level is to collect a star (or a shine). Once the star is collected, the level is over. One would think that removing the hallmark mini-games from the series would diminish the feeling of reward at the end of a level, but somehow the stars retain that feeling (at least for me). The mini-game, the reward and the purpose of the gameplay have now been combined and especially in SMS (I would say the most difficult of the 3D Mario games), you feel you have earned that star when you finally aquire it. This change in design might also be the influence of the new designers creating the 3D Mario series alongside Miyamoto. Yoshiaki Koizumi, Takashi Tezuka, Kenta Usui, and Takao Shimizu have all had design credits on one or more of these games, with Miyamoto taking a producer credit after SM64.
Well that's the history of Miyamoto's mini-games at the end of Mario's levels. I find it interesting how such a nice little reward system was developed and even taking to fascinating new places by other Nintendo developers (the Marioland and Warioland series), and i'm sure was used in many other platform games (the giant ring at the end of Sonic the Hedgehog comes to mind). The mini-game having been replaced by the star has not been needed for a while, but with New Super Mario Bros Wii on the horizon, we might see a resurgence of the end of level mini-game (I somehow don't think it's showing up in Super Mario Galaxy 2).