People can be myopic at times, thinking they know what's best for others.

Personally, I quite like the "helpful" as it stresses more the intent. I would typically not downvote even an incorrect answer given in good faith; but rather point out the (perceived) error. Then it can be either corrected or deleted (by OP). This is also what happened to me the one time (I know of/rememeber) I gave a truly wrong answer, and the few times I gave one that missed the point completely (due to some misreading of the question).

On the negative side, I sometimes got annoyed by what I would call "correct but very low quality" (some unexplained link to somewhere, and so on; no effort at all on the side of the answerer, and this also in cases where it was not some very busy top-expert on the subject giving some pointer, but more on general things). This is something I consider as problematic since it rather impeds some "better" answer being posted. (Things like this where a long time ago discussed under the somewhat different angle of "questions spoiled by comments"; though it is not exactly the same and the thing I currently describe is IMO rather more problematic). Typically, I do not downvote this either, but sometimes I think I should. Yet, the problem with downvotes is that as (I think) Noah Snyder once remarked a downvote can have the opposite of the intended effect (somebody will see the need to 'balance' it, and then one "downvoted" by +8). This is particullarly relevant in this scenario since sometimes it feels like such answers are given mainly to increase the point count.

General add on: while I do not downvote questions that much either, I would still like to stress that at least regarding me what was said above is for answers (as the subject indicates) not questions. And François G. Dorais said on questions not of questions.

To elaborate on this slightly the "official" description of votes is also totally different for questions and answers: for answers the criterion is 'helpful' (yes/no) for questions it is 'useful and clear' and 'not useful or unclear'.

By the way, it is very nice to see so many explications on the difference regarding voting in CW and non-CW :-)

There is or at least used to be some sort of convention that a downvote should be accompanied by an explanatory comment.

That's not entirely true. The only rule of conduct on MO is to be nice, honest and professional at all times. It is preferable to leave a comment by common sense: it's not nice to go about hurting people's feelings for no reason. Downvoting for obscure reasons is discouraged but not prohibited. Moderators will intervene if there is evidence that someone is downvoting for wrong reasons (vengeance, humiliation, discrimination, etc) or if this is part of a larger disruptive behavior.

A common use of downvoting is to indicate wrong or misleading information. In this case, a comment is in order since you do want readers to see the error. Another common use of downvoting is to indicate off-topic or irrelevant information. In that case, an accumulation of downvotes will have the effect of moving the post out of the way and commenting is not always necessary. Users should use their own judgement whether to leave a comment on a case-by-case basis.

Personally, I have no problem with people that are critical (and sometimes rather wished there where more on this site), however an unexplained downvote somewhere is not so much unfriendly or anything in this general category but often simply pointless in my opinion. Since the receiver reasonably might simply not understand what the motivation behind it was. (For example, it is still not clear to me for why I got my first downvote on this site meanwhile a long time ago; was it for the content or for editing something three times within a short period of time, or for still something else.)

So, if you intend your downvotes to have some "educational" effect I think it is better you explain them in addition. Even just the explanantion will have likely more effect than some downvote somewhaere.

To get back on topic: it appears to me you believe that an incomplete answer might deserve to be downvoted because it is incomplete (in the case of the Boolean algebras and probability measures question cited by Benjamin, you mentioned something I had already admitted, that I hadn't addressed the probability measures part [I had wanted to ruminate on that further before saying more], and presumably you mentioned that as part of your reason for downvoting).

For what it's worth, I don't think that's a good reason for downvoting. It's often the case here on MO, as in real life, that one has only a partial answer at hand, or maybe a partial answer is all one is willing to put up for public scrutiny at the moment. Such a partial idea may then go on to suggest an avenue for thought for someone else. The general idea is that those who are trying to make an honest contribution to MO are trying to be helpful in whatever way they can, and IMHO such efforts should be respected. On the other hand, if someone says something that is outright wrong, even while trying to help, then absolutely it is fair to downvote, preferably with an explanation as to what is wrong.

Edit: my general downvoting policy is consonant with Benjamin's. I feel no remorse in downvoting CW answers that I think are off. And I think correcting someone before downvoting their (non-CW) answer is the collegial thing to do.

Sometimes people might just simply click the wrong way. And, well, sometimes people just downvote something for completely unrelated reasons (fortunately not too frequent but some cases are on record on meta, and I am also pretty sure it happened to me more than once).