I've never used a site like this before--is up/down voting an expression of my agreement or disagreement with a statement, a statement on its helpfulness/appropriateness to the topic, something else altogether, or a combination of all of them?
There are no hard and fast rules - in the end, it's a community site, so everyone's votes are based on their own particular philosophy. However, in terms of how they are commonly used and best practices, read on. Please note that certain levels of rep are required to do anything from vote up/down to vote to close - if you don't see one of these options, you don't have enough rep to do it.
On a question, voting up tends to mean "That is a good question, other people should read this question, I'd like to hear answers to this question too." Voting down means "I feel this is a badly conceived question."
Remember you can also vote to close, flag, or delete. Vote to close if the question is an exact duplicate, off topic, subjective and argumentative, not a real question, or too localized. Flag if it is very low quality, spam, not relevant to RPG.SE, or otherwise needs mod attention. Vote to delete (high rep only) if something's already closed or flagged and needs to go away. You can do a combination of downvoting, voting to close, and flagging - flagging costs you rep but moves the question down, voting to close will take 5 votes and then close the question but you have limited close votes a day, and you can flag with no rep but mods generally don't act on small numbers of flags unless it's a clear and compelling case, preferring to let the community self police with downvotes and close votes.
Voting a question down probably shouldn't mean "I don't like that game system" or "I don't like that guy" or "I don't like that playstyle." Voting up probably shouldn't mean "Congratulations, you asked a question."
If you answer a question, you should probably be voting the question up as you are clearly engaged with it. Unless you are not answering the question, in which case you should at best be leaving a comment, as your answer is likely to get rightly downvoted/flagged for being "not an answer" (see below).
If you downvote a question, you should probably consider leaving a comment on it as to why so that the user can potentially improve the question and/or themselves.
Voting up has the immediate effect of upvoted questions "floating to the top" of appropriate views on the site, and other users seeing that a question seems good to other users and maybe they should check it out.
On an answer, voting up tends to mean "I agree with that answer" and voting down means "I think that is a pretty bad answer - I disagree with it or otherwise think it's off base." No vote means "that's technically a legitimate answer, but I don't think it's that helpful."
Remember you can flag answers, too, for being not an answer (really a comment or outside the scope of the question), low quality, spam, or not relevant to RPG.SE. In some cases you may vote down and flag; that's up to you - the voting down moves the bad answer down, which is helpful to others, but costs you rep. If it's spam you should probably save the rep and just flag it, as it'll get nuked anyway.
Voting up/down answers has the immediate effect of good answers "floating to the top" in the question and having more visibility to other users, it is a signal to them that "the community sees value in this question." In the end, this means that someone looking for an answer to that same question can easily see the ones everyone thinks is best.
On a comment, upvoting tends to mean "I like/agree with that." You can't downvote comments.
Upvoting comments signals other users that the community likes the idea within it, and makes them "float to the top" when comments are suppressed for space.
In the end, in addition to the functional effects of voting on promoting good questions and answers to the community's notice, the voting also generates rep for the user. You vote up someone's answers if you think they are making sense and should have loads of rep and be running the site. You let them alone if you're neutral. You vote them down if you think they're really not helping and perhaps just spamming answers to try to get rep. You flag them if they are spam or offensive or trolls or whackjobs or off topic or unsalvageably incoherent.
In a community where so much emphasis is put on reputation, a downvote is a serious thing. It is very unwelcoming for a new user to get a rash of downvotes the first time or two they comment. Too often I see the downvote used as a measure of agreement instead of fitness. If the answer is wrong or off-topic, then downvote and leave a comment why. But, downvoting just because they aren't part of the hive mind is just mean.
That leaves a three tier system: Upvotes for good answers and agreement, no votes for good answers that you don't agree with, and downvotes for incorrect or off-topic answers.
If people are still downvoting honest, on-topic opinions at the end of beta, then I doubt the group will survive. If a newbie sees an honest question or honest answers downvoted for no reason other than the answers express a different opinion, especially one they happen to share, then they will forever lurk, or forever leave.
Oh, and if you want your answer or comment to be read, then upvote the question.
This question also appeared on the main meta. I went there to see if there was a similar feeling before I posted here. https://meta.stackexchange.com/questions/480/when-is-it-appropriate-to-downvote/6467#6467
I have exactly the same point. The voting system is not for agreement/disagreement. Is for good answer/bad answer, and with bad answer it is intended an answer that is annoying or useless or technically wrong. If an answer is not useless, or not annoying, or technically sound, you should upvote it even if you don't agree with it.
On meta, however, traditionally +1 is for things you agree with, -1 for things you don't agree with.