As a "while a drink my coffee" poster, I sometimes post something that even I recognize later to be of little value. I'm not talking about flaming, just the occasional "hmm, I really didn't add much to this thread", or perhaps someone with more nimble fingers already posted the same answer.
As far as I can tell, there's no way to delete my own post. I can edit it, assuming that I can think of something intelligent to replace the original drivel with, but sometimes that's at least another cup away.
I try to catch most such posts before clicking the "Add Reply" button, but the option to delete my own post would be nice.