I know Nintendo doesn't focus on stories too much, nor is this place the biggest Nintendo fans(in which case just post your favorite Video Game story). But that's part of what makes them sometimes so Good in my opinion. My favorite is Punchout for Wii. Yes it's mainly a gameplay game, but it's a good, complete, boxing story of an underdog going on to become a champ to going on to leave the ring fighting on his own terms. With minimal cutscenes and mainly interaction from the player it makes you feel as if you were in the shoes of lil Mac as he went on to become a Lil Legend, all while mixing in tons of unique humor into the mix that'd barely be possible in any other medium except manga... or maybe it's just that ending cutscene that gets me.

Personally i say Xenoblade 1 (haven't played X or 2 so i can't comment on them), just has the right amount of depth and character interactions which i personally like.

Ocarina of Time easily

Probably one of the zelda games. Wind waker was my favorite.