At the moment we can choose to delete the branch when we merge a pull request, but when we decline a pull request, there's no such option and we have to manually delete the branch using a Git client if we want to.

[ Update on 2013-04-15 to make the request more clear to @Jens Schumacher from Atlassian ]
For example, when I want to *accept* a pull request by clicking on the "merge" button, I get this:

As you can see, there's a checkbox there that will make sure the branch gets deleted after the merge succeeds.

However, when I *decline* a pull request by clicking on the "decline" button (which is the next button on the right after "merge"), I get a very similar UI:

But as you can see, there's no checkbox there to allow me to choose if I want to delete the branch or not.