Two that could expand the discussion value:
If it happened to Halo then I'd expect the Nintendo fanboys to be crying "Metroid Rip-off" in the forums a lot, so I'll leave that one alone.
Rapelay.
All of a sudden it doesn't seem quite so controversial, does it? Bloody double standards.
Well, now I've got that out of the way.
Bioshock would have a whole new level of philosophy behind it if you were a female instead of a male, the whole concept of women's rights in those days would be one focal point there'd also be the whole thing with the Little Sisters which suddenly takes on a darker turn when you choose to murder them instead of saving them because when you're a male it strikes me as fatherly love to some extent, so I guess it can work as motherly love as well, which kind of opens up a massive can of worms if you think about it long enough, I mean some people could easily draw some parallels with abortion for one thing which only goes deeper into the rabbit hole.
The idea of being a woman in Rapture would also make certain scenes have more impact. The whole fight with Dr. Steinman ("What do I do with this one Aphrodite? SHE. WON'T. STAY. STILL!") would be more personal as he is mutilating "people" of the same sex that you are and I'd expect some people would get a chill down their spines when they hear him shout "SHE'S UGLY! UGLY! UUUUGGLLYYY!"
But maybe that's just me.