Spock gets a long-lost daughter with purple eyes who's an even better doctor than McCoy and when she arrives, Kirk instantly falls in love with her and makes her captain in his place. She takes them to the planet of the Sparkle Ponies where she defeats Khan with her beauty and that of her new glittery equine friends.
Heh! But also not so much heh, because here are some good cases made in that very article and several others within the same conversation, to the effect that 'Mary Sue' has become a lazy and insidious way of dinging on female characters disliked by the reviewer - most especially, female characters written by women - in ways which are both unfair to said authors, and in danger of limiting the public supply of awesome female characters. All sorts of subtleties of the true and false Mary Sue Effects are explored in these discussions, and I highly recommend all of them. In chronological order:
You Can Stuff Your Mary Sue Where the Sun Don't Shine, by Zoë Marriot (Aug 1st 2011)
Ladies, Don't Let Anyone Tell You You're Not Awesome, by sarahtales (Aug 4th)
Ladies Ladies Ladies, by blackholly (Aug 7th)
I Know a Little Girl and Her Name Is Mary Mac: the Misuse of Mary Sue, by seanan_mcguire (Oct 11th)
What Would Mary Sue Do?, by Zoë Marriot (25th October)
Here is my head hitting the desk, repeatedly.
My only real addition to the debate concerns the case where the name's deserved. I think one good test for whether a character is a genuine Mary Sue/Marty Stu or not, is whether they have the defects proper to their virtues - or, indeed, the virtues of their defects. If what is wrong with them has nothing to do with what is right with them, except to serve as a foil for the sparkly shininess of it, this is a warning sign. And if their most salient flaw is wangst, and yet they are in no other way anything of a wanker, that is an enormous neon warning sign flashing DANGER WILL ROBINSON DANGER !
At the age of thirteen, I independently invented the concept of fanfic and the character - but not, alas, the concept! - of Marty Stu, as a side-effect of the dire worldwide shortage of new Pern books. To encounter him at the age of thirty as a known public nuisance was both a revelation and a sort of relief, not to mention a salutary reminder. But if his sister is now being seen more often in pieces of vaguely girl-cootied speculative fiction than the Virgin Mary has manifested in pieces of vaguely toasted bread, then it may be that the pair of them are coming to the end of their useful work as Awful Warnings.
Either that, or Marty is going to have to start pulling more of his own weight. Which one, eh?