Okay, I'm tired of this. Here are the facts in order of "priority". I wrote some opinions in the details. Keep in mind that this isn't true only for NES, I'm just show that EVEN the NES has these properties I mention (also the number of pros and cons isn't important).
Pros
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It's a built-in and intended feature in the NES
I hope I don't need to write any details for this.
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NES games are capable of detecting that the game was reset through the reset button
For an instance, Zanac. The game has many cheat codes just like the level selection code:
Press 'RESET' button on your NES 13 times then press Start. Use Left and Right on the D-Pad to select the stage.
Here's adelikat submission:
#1344: adelikat's NES Zanac in 03:26.22.
Also there's 2 more cheat codes that makes use of pressing Reset for a various time (9 and 1).
One of them:
http://tcrf.net/Zanac. By the way this is a very useful webpage for TASers!
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Saves time in various games
Watch this page:
http://tasvideos.org/Movies-C3045Y.html
Note that most of them uses an input combination (mostly on the 2nd controller) to reset the game which isn't the same as pressing the reset button!
Cons
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It's not 100% verified that every NES hardware executes the same reset routine
Check out
http://nesdev.parodius.com for further info or
http://wiki.nesdev.com/w/index.php/Nesdev_Wiki about their experimentations and results.
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Save game data corruption (with the reset button) has a chance to fail on the real hardware
I tried to search for dissassembled games with saving data but couldn't find anything. I'm not going to details, I think you know why should it fail.
If the problematic cons will be verified on real hardwares, I will say that use the reset buttons to play games as fast as possible. Have fun.