I think the rule of thumb I'd go by is "Dress 1 level better than the person interviewing you." So, for example, if the office is "business casual," I'd recommend "business formal," suit (or at least a jacket), tie, etc. Of course, if the office were business professional, there's not much to advance to unless you did black/white tie, so in that case still being business pro would be the way to go.

I know that when we're interviewing people, clothing isn't the most important aspect that we look at, but we DO look at it. If you dress like you don't care, then we think (even if somewhat subconsciously) that you don't care, so why should we hire you?