What is the policy, or what should the policy be, regarding own answers that are correct, but have no up-votes.

Obviously, if you have no up-votes, then nobody find your answer interesting or good enough, even if it is correct.

Should we then delete such answers, to clean up the database? Or should we let them be for the sake of completeness?

EDIT: Not enough answers to draw a final conclusion, but I will personally follow Stephan Lehmke’s recommendation. Therefore, I accept his answer.

Sometimes it happens that the answer is a no-brainer, e.g. update the problematic package, forgotten ; at the end of a line in TikZ, etc. In such cases the answer is in fact a comment and it is hardly worth to bother converting it into a proper answer. IMHO these are candidates for deletion by the OP.