Should only correct answers be up-voted, or is it ok to upvote incorrect answers where an attempt has been made and well explained, despite it being wrong.
If only correct answers can be upvoted, should I downvote incorrect answers or leave them?
What do you guys think?
In the case of "solve this puzzle" questions, upvote any answer that you think contains an insightful answer to the question. Even if it's wrong, there must be some value in it if you're even considering voting up. In the case of certain (kinds of) puzzles, a "wrong" answer may mean "not the canonical answer". In others, an answer that misses one "rule" might reach a very interesting alternate conclusion.
Of course, remember that this isn't a social site; an upvote doesn't mean "I like you and want you to get points" or "good job, you tried". Upvote answers based on the quality of the answer alone.
The bottom line, though, is that there is no proper way to vote. Upvote answers you think have value, downvote ones that don't. The community will vote their own opinion, and one or two weirdos will be drowned out if an answer is obviously one way or the other.
I don't think it makes any sense to upvote wrong answers. The purpose of stackexchange is to provide correct answers. This is true even for puzzling.stackexchange. And it is the purpose for the upvote/downvote system to motivate users to write good question and answers.
If an answer is not correct it can be repaired by the poster (or anyone else). Even if it cannot be turned in a full answer it can changed in a partial answer that does not contain wrong statements. If the answer is repaired you can revoke your downvote. You can even upvote the answer now.
If you will upvote wrong answers, their posters will not be motivated to change them. Even worse, it can motivate the poser of the question to accept the wrong answer because he thinks that is a correct answer. Especially if it is a complex answer that the poster of the question does not understand fully.
