In deviantart, is it possible to delete any posts you make?

Joony, are you talking about deleting a post/comment or deleting a submission?
If you're talking about deleting a comment, I don't think you could do that - although there's some kind of 'pencil' icon on the top right side of your deviations and profile comment's posts specified for hiding each posts or flagging it as a spam.

But if you're talking about deleting submissions, Exilement has answered it then. :)