I have a server that I'm taking down. The only thing I have left to migrate is my repository. This server is listed as the origin (master) for one of my projects. What is the proper way to move the repository to keep the history.

To add the new repo location,

git remote add new_repo_name new_repo_url

Then push the content to the new location

git push new_repo_name master

Finally remove the old one

git remote rm origin

After that you can do what bdonlan said and edit the.git/config file to change the new_repo_name to origin. If you don't remove the origin (original remote repository), you can simply just push changes to the new repo with

git push new_repo_name master