So, this is part of a procedure I do quite often so I can learn the basics about writing a videogame story (I've come to call it "Story Testing"). The idea is mainly about taking the theme (meaning style, gameplay mechanics etc.) of a game and the story (which means characters, general story or even dialogues) and think about interesting ways of how you could tweak or improve these elements to make a better game (obviously this is very subjective and a good story can differ greatly from person to person).
For example, I've been looking at some trailers for The Wind Waker HD (which will be released in October) and I've been thinking that a pretty cool character that's been missing from the game is the romance of Link's sister. I imagine him as a kind of a goofy guy (kid really) that after Link's sister has been taken he embarks on a journey of his own to save her. Link could meet him at certain points in the game (for example at Windfall Island) and he could act as a funny "wanna-be-of-help" character but that could give Link viable info on certain occasions.
Another idea, I've had since childhood, is a game where Wario (instead of Bowser) abducts princess Peach and asks a ransom from Mario to set her free.
Over the years I've had a great number of ideas of how a game's story could improve and I think it's a great exercise to think "outside of the box" and in the process become a better writer yourself. So, I'm posting this topic as an "inspirational ground" where we can use existing stories and characters to learn the essential principles of writing. If anyone else has some ideas that he thinks would make for a(n) (more) interesting game, or has some feedback for ideas already posted, please set your mind free below.