Mary-Sue characters that you can't help but love anyway.

My favorite character in all of Star Wars is Kyle Katarn from the Dark Forces / Jedi Knight series. Whilst I've always thought he was a badass, someone referred to him as a Mary-Sue the other day and i can't believe i didn't see it before!

• Overly complex backstory: He was an Imperial stormtrooper, who turned into a smuggler, who is actually a Jedi, but is grumpy about it unlike those boring 'normal' Jedi.
• Secretly as important as the 'main' characters: Originally he was the one who stole the Death Star plans that made it's destruction at the end of Episode 4 possible.
• Doesn't obey the rules of the setting: Can use Dark side powers without corruption (and canonically uses force-choke at least), with the explanation that "powers aren't inherently good or bad, it's how you use them".
• Morally ambiguous: Loopholes any dark side points from killing a defeated opponent in cold blood by pulling a Pick. It. Up. Despite this explicitly being a major contributor to Anakin's fall.
• Overpowered in combat: Famous for killing multiple Kell Dragons barehanded. Beats a laundry list of Sith lords, destroys multiple imperial bases and ships.

Now some of this can be excused a little as being a video-game character, however looking at that list it's pretty inarguable he fits the criteria for a Mary-Sue. And yet for some reason i will never stop ranting about how awesome he is to anyone who will listen.

So that said, who are the Mary-Sue characters that you love despite it all? And what exactly is it that gives some characters a pass where others can be completely immersion breaking for the same reasons?