I think the GM is entitled to a "line of credit" with regard to my character, increasing in proportion to how well we know each other, the necessities of the game, and the degree to which the proposed elements jibe with the starting concept. I also feel I have the right to say, "No, you've overstepped. That's not my character."
With that in mind, I think there are certain areas where this usually works well. Long-lost brothers... as long as it's reasonable for my character to have a long-lost brother based on the background I've already provided, this seems almost more like a campaign event than a characterization, so that's okay. I'm playing a cyberpunk game and I find out I'm a clone/the product of fabricated memories/an android who thinks it's a person/a person in a simulation? Yeah, that's okay, too, I think. That would be as much as a surprise to my character as to me, so it doesn't retcon the authentic emotional experiences I have invested in my character. I'm adopted? Probably jarring in many cases, but probably okay, and perfectly in genre if I'm playing a historical WWII game, or a courtly intrigue game, or some game based on prophecies and whatnot.
Thigns that are not okay without my permission (short list): declaring my character is a comic book style mutant rather than a highly trained super-normal; stating I have a relationship with an NPC that would have required some kind of active involvement on the part of my PC (fiance', old mentor, estranged parent, etc); revealing something about my character that I should had knowledge of (not-so-long-lost brother, identified at an early age as a child of prophesy); rewriting my stated background, even to a small degree; any emotional reaction to anything not dictated by involuntary, mostly physiological processes, preferably ones codified in the rules. And naturally, anything I feel goes beyond your "line of credit" whether you agree or not; fix it or I start to lose interest in the game.
Correct: "Do you think your character might have trained with a master of the Northern School?"
Incorrect: "You recognize at once your old master, estranged ever since you refused to heed the edicts of his martial tradition."
Correct: "So you see, Joe. Everything you ever thought you were, that's just a story we made up so you would feel okay about yourself. You were always made for one purpose."
Incorrect: "You watch in horror as your small halfling arm transforms into a writhing tentacle. 'Now you know who your true father is, halfling,' roars the mad sorcerer. 'Yog-Sothoth! Yog-Sothoth!' Your loyal companion turns to you and cries out, 'No, Master Frodo! You mustn't believe him! He's lying. I know who you are! It's not this... this thing!' What have you done to him, you monster?' The sorcerer chuckles. 'Oh, come how, Samwise. It's time to drop such pretenses. I got to you a long time ago.' You recall, with increasing rage and sense of betrayal, that one night under the hill, when you were in each other's arms, and have not spoken of since. Suddenly, it all makes sense, and you barely restrain your urge to kill your once boon companion. Your strange, alien limb responds to your rage by writhing with almost lustful anticipation of the carnage you so desire."