It occurs to me that one of the problems a lot of gaming groups have is a lack of understanding between the GM and the players. Yes, I know, big revelation, but I mean it in a specific way: the GM doesn’t understand what the players consider to be the important bits of their characters.
I suspect this problem arises more in groups that have at least a little social roleplaying, as opposed to the people who refer to their characters as “my guy” or “Bob 3” and track nothing more in depth than the equivalent of runs batted in. Still, it is not impossible that the player considers Bob 3’s flaming sword to be an integral part of his character, even through the frost brand dragonbane sword does more damage.
Consider GURPS disadvantages like Albino and Nightmares. A player who takes these disads is likely doing it for flavor, despite the mechanical issues the character will have later (unless he really needs the extra points, or thinks the GM won’t enforce the penalties, or both). The GM should keep track: does the player work the disad into the character’s backstory? Does he immediately begin planning to save up points to buy it off–that is, he just needed the extra points in character creation, when they’re worth more? At some point does he have the points to buy it off, and nothing else urgent to spend them on, but leaves it anyway? If the player wants that disad for flavor, it would be impolite of the GM to, essentially, inflict a cure on the character. A lot of what the player likes about that particular character could easily be bound up in something that is technically speaking a disadvantage.
Similarly, a player who likes working with the tension between his character’s secret identity and mundane life isn’t going to thank a GM who has a supervillain kill off the PC’s family. Sure, he doesn’t have to worry about getting home for dinner after crimefighting any more, but that was part of the fun of it for him.
The converse of this problem is the player who regards everything on his character sheet to be sacred. Mess with anything down to the blanket in his pack and he’ll sulk and whine. God forbid you offer him a chance to resolve his character’s angst; even though he won’t take you up on it, he’ll assume you meant to wrest control of the character from him. These are the folks who get peeved when the supervillain so much as mentions one of their Dependants, never mind that they got points for them.
How to resolve this conflict? The simplest way I can think of is for the GM to ask before making significant changes, or to ask when the campaign begins. This can lead to problems with the whole-sheet approach, however, as it’ll lead to the GM having nothing she can mess with. Maybe, then, what’s needed is something like what the NFL did with the expansion draft: there’s a short, say 3-item, list of things that can’t be played with without explicit permission, but everything else is fair game. It doesn’t have to be specifically mechanical things, either; for instance, in D&D neither albinism nor the PC’s dependants are actually on the character sheet.