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Tober said:

Super Mario All Stars for the SNES. A collection of great games now included being able to save progress, keeping the great play ability of the NES originals with even more vibrant colours.

This is a great example. 
The feeling of the games vary a bit so if one is used to play the original versions the All Stars versions of at least SMB3 is not as snappy. 

The complete upgraded graphics and added save functions was such improvements that one could use it as a gold standard for remakes. 

Also need to mention the fun battle mode that was added as well, and the first release of the second Super Mario game outside of Japan. It was a great compilation of remade games for the new hardware.