Often, it belongs to the other players.
I recently started playing in a new campaign of All Flesh Must Be Eaten, Eden Studios' RPG of zombie survival horror. I planned for my character to be a skilled professional -- not a doctor, soldier, or something useful like that. My idea was for a cable TV installer. He would have seen a lot of interesting and weird things already by going into people's homes (I know a few real-life satellite installers), and would be an expert in electronics.
The other part is that I wanted to model the character's personality after the TV character of Ron Swanson. He would know a little about everything, and be very secure in his opinions (but with room to grow), all good hooks for role playing. He would also have a Ron Swanson mustache. And that's how I lost control of the character.
Once the other players start discussing his mustache, and the fact that he has a van... any serious ideas about the character among the other players disappear. The idea of the character that you had intended is replaced in the minds of the other players by the ideas that they have discussed -- or joked about -- around the table. That becomes the character they react to in game, from then on. This isn't necessarily a bad thing. However, it is something to think about when planning your character and his/her personality. Certainly, it's on the same level as a GM trying to develop names for NPCs that can't be twisted around into jokes by the players.
How might this play out differently at the table? What could you do to change this?
Think about your character's initial impressions and play them out. Plan to work your ideas about your character's personality into the game from the first session. Take opportunities and risks in games to show what your character is like to the other players. Then do this every session. One of the best pieces of player advice that I've been given was to think about how to work your character into the story at the table. I tend to be passive as a player, in the background, and wanting to get other players into the spotlight. Sometimes, you have to take a leap -- make a decision, take an action, be bold. There's a fine line between being an assertive player and being disruptive. Don't be disruptive or demanding. But if there is trust at the table, jump in.
Tell the other players -- in game -- what your character thinks about. Ben Robbins wrote a great post about character monologues. Not necessarily dialogue, but actions and thoughts in the character's head. Get these out at the table in play. Your character has traits, advantages, flaws... whatever the system might call them. They might be on the character sheet or in the character background you wrote, but if you don't work them into play, or tell the other players about them, then they may as well not even exist. They don't truly become part of the game until they are worked into the shared experience of all the players.
Any others that I missed?