I like Jay Elston's answer format, but disagree with several of the points.
Specifically, I think usefulness means in general, not just for me.
For Questions, the qualities the hover-text says it is looking for are:
...shows research effort; it is useful and clear
I don't vote up questions based on whether I need the answer or not. I simply vote up based on if I think future users will benefit from the question.
As an example, in the question Block elements vs inline elements in HTML: why the distinction? I even made a comment to that point. The question posed a dilemma which I actually didn't believe to be a problem at all, but I have worked with many programmers who ask these types of questions, and it was asked clearly, therefore it deserved my upvote.
I vote down if, as the help text says, it doesn't seem like an answerable question, is a rant instead of a question, is confusing or pointless. Roughly, it's the opposite of the above: if the asker doesn't seem to have the goal of asking a question which might benefit others, then I vote it down.
Also, please don't down-vote just because the question has been asked before! That's what close-as-duplicate is for, and it's not a bad thing. If it's blatant, then it probably doesn't "show research effort" either, so vote based on that.
For Answers the hover text simply asks if the answer is useful.
That's basically all I consider. I consider my vote for what it is — a tool to push the answer up the page and give a mark of agreement.
The answer must be right — this means that if the answerer posted some good and some bad advice, I will not vote it up. In addition, I don't consider it to be right unless it paints a sufficient picture — if the real truth is that A is probably the thing to do, but the user might beware that sometimes it could be B instead, but the answerer only said "Do A" with no context, then I don't vote it up, or I might even vote it down.
Essentially — if the answer guides the reader in a good direction, I vote it up. If it guides the reader in a bad direction, down it goes. And no vote if I don't think someone is either helped or harmed by reading it.
Your other questions...
Do you want that every question/comment/answer we read are categorized in our heads?
Like I said above, for most I think you should at least categorize them in up/down/neutral. Therefore, you don't vote on all of them, but if they are either up or down, you should use your vote.
Do you want more people to reach their voting cap?
I think they'd love it if everyone reached their voting cap. I read so many neutral questions and answers that I rarely do, though (and by neutral, I mean I don't feel good about pushing it either direction, so I feel like I would be doing a disservice to choose one).
What percentage of read questions sounds like a reasonable one for voting (forgetting the up down issue at the moment)?
Putting aside the issue of not knowing enough about all topics — if it's a tag you know very well, I'd roughly say you could vote on, answer, or vote-to-close at least 50% of questions.
Should people be clicking into questions they think are bad, just to down vote them?
If they really are bad, yes! That is absolutely a community service.