This is kind of an open-ended topic with many layers but I think I will start it off with something simple: how much free reign do you give players to write stuff in their background or propose things during the game about the setting? In my experience, character creation always involves lots of back and forth. This comes from my days as a Storyteller in the White Wolf system, which encourages the group to engage in a series of "Prologues," mostly solitary pre-adventures where each player takes turns with the Storyteller going over stuff in their backstory. This might be a simple conversation about the character's life before the game begins, it could consist of a personality quiz or a series of "what if"s and "how does your character feel about X?" type questions; or it could mean actually roleplaying pivotal events that shape your character's view of the world and of himself. In a game like Werewolf or Vampire, particularly relevant to that conversation would be how he or she experienced the First Change or the Embrace.
So I have a lot of experience with it as more of a collaborative effort to figure out who the character is, what makes him tick and what his place in the world might be. In D&D, I take that conversation as a prime opportunity to brainstorm about secrets or goals the character might have, but also give the player opportunity to come up with some of his own stuff to leave a mark on the setting. Maybe he or she trained at a martial academy and has specific ideas about the kinds of folks in his graduating class, his instructors, what happened while he attended, etc. I welcome contributions like that to the setting. It's less work for me, after all. Obviously everything has to be approved but I think it makes players feel like they are contributing something meaningful to the ongoing narrative. The game belongs to them, too.
On the other hand, after the game starts, I feel a little differently. I don't know why but I am much more reticent to endorse recommendations after we have been playing for even a single game session. I don't have a very good reason for this, I'm just way more skeptical about stuff like that and the only exception is if someone is creating a new character to bring into the game. In that case, they get the same wiggle room to innovate as someone would at the beginning of the campaign.