My worst answer was "I don't know." I've since learned that "it depends," with a couple of examples, is perfectly appropriate. And that's how I'd answer this one:

Are you willing to put the interests of X Company ahead of your own? It depends. I would put important interests of the company over minor interests of mine and I would put important interests of mine over minor concerns of the company.

Of course then they will ask what if both are important. Then I hope I'd say that maybe the the job and I aren't a good match. I try not to get into situations where that would happen. And can they give me examples of where this has happened before?

I'm to the point now where I'm always trying to guess what their real goal is. If anyone even asked me illegal questions like "Are you planning to have children?" I'd just say something like, "It sounds like you're worried that an employee might quit just when you finally got them trained. I wouldn't take this job if I didn't think I'd be wanting to stay a while."

And if anyone asks me those evil "worst weakness" types of questions, I ask a similar one right back, like what is the worst weakness of the company or section of the company. Or just give a brief answer: Has anything ever irritated you about people you've worked with? "Of course."