Other than some basic characters, what's the story of Mario?
Zelda is very narrative driven. Very very easy to fuck up.
it depends on the zelda. some zeldas the whole story can go on a note card.
almost all the rest could go on an IMDB synopsys of a couple paragraphs.
it depends on which link, which zelda, which setting, and then what arc to do in those. Personally i kind of feel like ocarina of t ime does one of the best jobs (storywise) of showing a start with a character who plunges into a world they didn't know, and then master some things to unravel some mysteries and then delve into them to save the day. maybe wind waker.
a lot of zeldas arn't so hot for heroes journey or "lets explore this new world with the main character" as well.
though i think it would be quite easy to adapt any of the frame work of any of the worlds, and slap some characters, discovery, ups and downs and have a cool story.
BUT...i can almost promise you that no american film studio is going to make a story ab out one white dude having a heroes journey. just like in the mario movie where they had to have mario tagged along by the princess to show him up here and there, a toad, a monkey, and a wider cast, they will put it in. It's a shame too because the story of one young man on a journey , gaining confidence and facing down evil is one of the most timeless stories...which i guess post modern fucks are trying to snuff out so you buy next product and eat the boogs.