According to this FAQ entry, the only restriction on self-deleting an answer is that you can't delete an answer that's been accepted. But I've also heard of users getting in trouble for deleting (non-accepted) answers, and there's the CC-SA license to consider, so -- quite aside from what is technically possible -- my question is when it's permitted to delete your own answer.
Some cases to consider:
You now believe the answer is incorrect.
Your answer is correct, but another answer covers the same territory better.
You aren't satisfied with the quality/rigor of your answer, e.g. it's speculative and you didn't back it up (on a site that expects that).
Something in the answer embarrasses you and you'd rather just make it go away.
Your answer wasn't well-received by the community (whether that's "meh" or "make the rep bleeding stop please").
(I'm sure there are others; this isn't meant to be an exhaustive list.)
Does voting matter, either in absolute terms or in comparison to other answers? For example, maybe it's ok to delete a lower-voted one but not the top-voted answer, or one with score > N??
There is a badge, Disciplined, for deleting your own post of score 3 or higher. This tells me that it's sometimes ok to delete upvoted answers. But I'm not sure how much policy we can infer from badges.
Could we have some clarification please?