I think one of my favorite genres of remakes is the extend and redefine. Zero Mission is excellent at this and I imagine one of the earliest to do this. It takes something so familiar in the original Metroid, but immediately lets you know that this version will take it's own path. It leads you on, until it breaks open the formula and provides you with a completely new experience. There is also a certain maturity that is added to a game that had little to no sense of purpose.