Your Xbox 360 avatar lives on your Xbox 360. And the internet. If you'd like him or her to live on a shelf in your office as well, you should speak to custom toy company FigurePrints.
For USD$50 they'll take your avatar and produce a figure replicating its appearance and dimensions. The only catch is you have to select from a number of pre-determined poses and they can't print any licensed material (so NBA jerseys or game-related gear is a no-no).
This is the same company that's made a name for itself building World of Warcraft figures based on people's avatars.