How do you stop tracking a remote branch in Git?

To remove the association between the local and remote branch run:

git config --unset branch.<local-branch-name>.remote
git config --unset branch.<local-branch-name>.merge

Optionally delete the local branch afterwards if you don't need it:

git branch -d <branch>

This won't delete the remote branch.

To remove the upstream for the current branch do:

$ git branch --unset-upstream

This is available for Git v.1.8.0 or newer. (Sources: 1.7.9 ref, 1.8.0 ref)

source

As mentioned in Yoshua Wuyts' answer, using git branch:

git branch --unset-upstream

Other options:

You don't have to delete your local branch.

Simply delete the local branch that is tracking the remote branch:

git branch -d -r origin/<remote branch name>

-r, --remotes tells git to delete the remote-tracking branch (i.e., delete the branch set to track the remote branch). This will not delete the branch on the remote repo!

See "Having a hard time understanding git-fetch"

there's no such concept of local tracking branches, only remote tracking branches.
So origin/master is a remote tracking branch for master in the origin repo

As mentioned in Dobes Vandermeer's answer, you also need to reset the configuration associated to the local branch:

git config --unset branch.<branch>.remote
git config --unset branch.<branch>.merge

Remove the upstream information for <branchname>.
If no branch is specified it defaults to the current branch.

(git 1.8+, Oct. 2012, commit b84869e by Carlos Martín Nieto (carlosmn))

That will make any push/pull completely unaware of origin/<remote branch name>.