I have a question that I submitted an answer to, and it ended up getting 3 downvotes (I won't post the link here because I want to avoid a discussion on the specifics of that question and answer). On a site like stackoverflow.com there would be no question: I would delete the answer without hesitation. However, with a site like japanese.stackexchange, the situationis different. There is no absolute yes or no answer, and unless it's an etymology question, people can only go by their experience and individual teaching, which can vary greatly.
In general, I try to avoid deleting anything unless I know that it clouds the site with misinformation and useless or irrelevant content. For an answer that got down-voted, I simply look at it as "my two cents" that many people just happen to disagree with. The OP or the reader will see that the question was down-voted, and appropriately take what I say with a grain of salt.
In general, I feel that deleting information does not help the site mature, but I would also not like for the site to be clouded with misinformation and useless content. If other people were of the same mind as me, it'd be good for them to see that someone else thought the same thing that they did (and were probably wrong, of course). I'd like to know what you all think. Do you think that it's best to leave down-voted questions up, or delete them?