To delete a local branch

git branch -d the_local_branch

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To remove a remote branch (if you know what you are doing!)

git push origin :the_remote_branch

or simply use the new syntax (v1.7.0)

git push origin --delete the_remote_branch

Note

If you get the error

error: unable to push to unqualified destination: the_remote_branch
The destination refspec neither matches an existing ref on the remote nor
begins with refs/, and we are unable to guess a prefix based on the source ref.
error: failed to push some refs to 'git@repository_name'

perhaps someone else has already deleted the branch. Try to synchronize your branch list with

git fetch -p 

The git manual says

 -p, --prune
           After fetching, remove any remote-tracking branches which no longer exist on the remote.