Whatever the system or the world used, what can a player add to his character background that will help the GM make the game more interesting.
Games are much more interesting with the addition of the character's events/NPCs/whatnot into the main plot(s). Much like Anime, where all the character back stories somewhat interact, it created a sense of wonder. The plot gets richer, the world felt more alive, and mostly the players feel like they are building the story or at least influencing it from the start. Sometimes, I pulled it off, sometimes not so much. So, I am looking for way to make things better for the GM.
I realise that the question is vague and is asking for techniques rather than solid facts but I believe it is a useful question nonetheless -- we shall see how fast it gets closed ^_~