Apologies -- someone else was asking about PM's, I misconstrued.
Just out of curiousity, I saved, edited and deleted a post. It appears to delete a post, you click the Edit button first, then from that box, you will see a Delete button. And you'll have to give a reason why you're deleting, but it appears the post does go away.
From the Admin's post at the top it appears only Classifieds allows that, the other areas likely do not.