Executive Summary

$ git push -d <remote_name> <branch_name>
$ git branch -d <branch_name>

Note that in most cases the remote name is origin. In such a case you'll have to use the command like so.

$ git push -d origin <branch_name>

Delete Local Branch

To delete the local branch use one of the following:

$ git branch -d branch_name
$ git branch -D branch_name

Note: The -d option is an alias for --delete, which only deletes the branch if it has already been fully merged in its upstream branch. You could also use -D, which is an alias for --delete --force, which deletes the branch "irrespective of its merged status." [Source: man git-branch]

Delete Remote Branch [Updated on 8-Sep-2017]

As of Git v1.7.0, you can delete a remote branch using

$ git push <remote_name> --delete <branch_name>

which might be easier to remember than

$ git push <remote_name> :<branch_name>

which was added in Git v1.5.0 "to delete a remote branch or a tag."

Starting on Git v2.8.0 you can also use git push with the -d option as an alias for --delete.

Therefore, the version of Git you have installed will dictate whether you need to use the easier or harder syntax.

Delete Remote Branch [Original Answer from 5-Jan-2010]

From Chapter 3 of Pro Git by Scott Chacon:

Deleting Remote Branches

Suppose you’re done with a remote branch — say, you and your collaborators are finished with a feature and have merged it into your remote’s master branch (or whatever branch your stable code-line is in). You can delete a remote branch using the rather obtuse syntax git push [remotename] :[branch]. If you want to delete your server-fix branch from the server, you run the following:

$ git push origin :serverfix
To git@github.com:schacon/simplegit.git
 - [deleted]         serverfix

Boom. No more branches on your server. You may want to dog-ear this page, because you’ll need that command, and you’ll likely forget the syntax. A way to remember this command is by recalling the git push [remotename] [localbranch]:[remotebranch] syntax that we went over a bit earlier. If you leave off the [localbranch] portion, then you’re basically saying, “Take nothing on my side and make it be [remotebranch].”

I issued git push origin: bugfix and it worked beautifully. Scott Chacon was right—I will want to dog ear that page (or virtually dog ear by answering this on Stack Overflow).

Then you should execute this on other machines

# Fetch changes from all remotes and locally delete 
# remote deleted branches/tags etc
# --prune will do the job :-;
git fetch --all --prune

to propagate changes.