We've had a few questions recently by new users which were well-formed questions that just weren't good matches for our main site. That's understandable, since the askers are often not familiar with how our site works, and we have some rules as to what sorts of questions are allowed that might be stricter from different sites. For instance, we don't allow recommendation questions and our policy on questions asking for lists is fairly complicated.
Recently, people have been downvoting these questions. An example* is https://anime.stackexchange.com/questions/2645/im-looking-for-a-list-of-humorous-anime-similar-to-oruchuban-ebichu. This is a well-written question which is interesting, but doesn't meet our site criteria. So it should be closed. But downvoting in this case will only drive away a new user who could probably productively contribute to our community. It's currently at -4, though I'm contemplating upvoting it just because I don't agree this question should be at -4.
A downvote essentially conveys the message "you should have asked a better question," but the only way the user could know that question was bad is if they had read some obscure meta thread with only about 100 views. Practically speaking, a meta post with 100 views has only been seen by at most 21% of our current registered users. Expecting new users to read every meta thread just to ask one question is ridiculous, especially since many of them don't even know we have a meta site.
When the asker makes these sorts of honest mistakes, you should leave a comment explaining (nicely) why the question isn't a good match for our site (referencing the relevant meta posts), and direct them to chat where such questions are welcome. If there is already such a comment, upvote it. If you can vote to close, then do so.
But if the only way the user could know that the question wasn't allowed is to be an active user here (and they aren't) then don't downvote it. New users will see this as an attack on themselves and will be unlikely to return, and we aren't anywhere near the size that we can afford to be turning away interested new users.
There are cases when a new user's question is completely out of order. These are things like spam, "What's your favorite X?" questions, and questions which violate the Stack Exchange Terms of Service (e.g. posting pornographic images). In these cases it's acceptable to downvote, though you should still probably explain why in the latter two cases. But if the user has just misunderstood our site's particular policies, downvoting them is only more likely to convince them that they are being attacked, which will just make things worse.
tl;dr: Don't downvote new users who make understandable mistakes, but do point them to our policies so that they won't make the same mistakes again.
*: Yes, I'm aware that the OP in this case has been on our site since private beta, but he clearly isn't an avid user. For all intents and purposes he's basically a new user.