My answer: It depends on the (usually implied) "contract" of the game.
I have two modes I DM in: 1) casual, 2) intense. The latter is reserved for my homebrew world while the former is always what I use for published settings (Greyhawk is my usual choice, FWIW).
In the case of Greyhawk, the character is always the player's property. Anything other than that is absurd. Heroes come and heroes go. A few legends may spring up, but nobody really cares. Once the player leaves the game, the character is never heard from again. Anytime the campaign is reset, we go back to the way the setting book presents it.
My homebrew is very much different and I make no secret of this to my players. The PCs in my homebrew have free license to enact massive changes to my setting. In fact, I endeavor to present the opportunity to them. The world will mold to them and their characters names will go down in history.
There are still many characters as old as 20 years, real world (400 years, game time) who are legendary to current players and characters. None of the current players in my group are part of that first group, but they are all familiar with some of their exploits.
The trade off for this is that characters created for my world are a part of my world. That you for your contribution. You will be recognized for it whenever possible, but your character is a derivitive work of my world and I'll retain all applicable rights.
I have but one world that I develop and add depth to. A player has many characters over his career. Please be respectful of that difference and leave your character where he belongs. If I'm going to write your character into the history of my world, you need to write my world into your character.
A note on this, though. I'll only NPC a retired character that I feel _very_ comfortable with. If the player wants to pick up the character again, it's his right. This is where I've gotten into running a god game before -- the character was retired into godhood and a couple of years later, the player said, "Gosh, I sure miss playing him."
Basically, I define the sandbox, but the player always has the right to pursue any course of action within that sandbox. If you create a character for my homebrew, I expect it to stay there, but you'll always have control while you stay there. For all intents, the character will not be played without both of us there.
The difference between the casual game and the intense game is whether the stories are retold in character of out of character.
FWIW, I almost always consider email games to be casual games. They are just too much of a mixed bag usually. (There are, of course, exceptions.)
The flip-side to that is that you can run a character that is wholly yours and I really don't care what happens to him. Of course, he'll never be more than a bit player in the grand scheme of things and his name will never be written into the history books. He'll be a sidekick and all the limelight will go to the PCs who are agreeable to the other contract.