Answer is wrong
Yes, of course.
Answer is misleading (may be technically accurate, but will lead to readers making mistakes)
Yes, of course.
Answer doesn't match the question (e.g. a C# answer to a question about Java)
Usually. If it's really that far off, then yes. If it explains something that someone with the same question could reasonably be expected to need to know, the probably not.
Answer doesn't really address the question, e.g. suggesting a completely different solution, even if the question specifies that there are good reasons why the current approach has to be followed
It depends. It's important to have answers to questions as asked, so that they can be looked up. Answers don't only exist for the person who asked the question; in fact, that person is just one out of arbitrarily many, and not any more important than the others. Just because someone had an XY problem doesn't mean that nobody else really needs to do the ordinarily-inappropriate thing that was asked about. For that matter, the person who asks is not required to actually have the problem being asked about.
On the other hand, when there is potentially an XY problem, it's really important to clarify the question.
Answer is okay, but not as good as another one which currently has fewer votes
Answer appears to be plagiarised from existing answers.
Yes, but this should also be flagged. Plagiarism is against the rules and Stack Overflow in particular has a dedicated flag for it. On other sites, use a custom flag.
Answer is by someone I don't like.
No. That becomes serial voting, which is against the rules (and the system will also try to correct it automatically).
Answer is abusive (profanity, spam etc).
These are different things. If it's spam, or if there's a Code of Conduct violation - i.e., the profanity is directed at a user or a group of people etc., then downvote and also flag.
If there are just some naughty words and everything else about the post is fine, then edit them out and consider leaving a comment.
No reason, I just felt like it.
No, of course not.
I'm a Happy Vertical People Transporter, and prefer down to up. Have you considered down?
No, of course not.
Ideological grounds: answer suggests a technology I don't like, or expresses a negative opinion of a technology I do like
Sort of. Answers that suggest needlessly insecure approaches (such as inappropriate uses of
eval in Python, or approaches that would introduce an SQL injection, buffer overrun etc.), or which represent a "cargo-cult" workaround that avoids a proper understanding of the problem (attempting to fix import problems in Python with
sys.path hacks) get downvoted. Answers should not express opinions about technologies at all; please edit that out.
I don't know if this concept has meaningful analogues on other Stack Exchange sites.
Answer is addressing a low quality question that should be closed or marked as duplicate.
Absolutely yes. People who answer such questions must receive a clear signal that they are doing something wrong. Users who routinely do this sort of thing are abusing the system and acting directly contrary to the site's goals, seeking a perverse incentive. Such answers also interfere with automatic cleanup of Stack Exchange sites via the "Roomba". It's the least I can do to chip in my -2 reputation and a sternly worded comment, to combat those who are seeking a quick +25 and don't care about the site's goals.