A little humor can work, too - one of my responses to "What is your biggest weakness?" was a (truthful) "Well, I'm not that mechanically inclined, so I'm probably not the person you'd want taking the copier apart to fix it." Not altogether flippant, because I was the key contact for equipment maintainence in my last job. I just knew when to call in the pros.
Another thing, more serious - don't forget that when you interview, you're scoping the company out to see if you'll like working there, too. I had one interview earlier this year for a job that seemed to be a perfect fit for my skills and experience, with an organization that does good and valuable work - but within five minutes of the interview, I knew I wouldn't be able to work with the person interviewing me, who would have been my manager. Our personalities just would not have meshed. I was ready to turn down the job if it was offered, but before I could, I was offered the one I have now.
As for questions for them - if they didn't bring it up in the interview, ask how the job came to be available. That's important. One of the nastiest situations I was ever put in was replacing a secretary who the department had not wanted transferred and was determined to get back at any and all cost. It's no fun being "that temporary secretary who stole our Bev's job."
The worst question I was ever asked? No contest. It was a slightly sneering, "So did your father get you all of your jobs there, or just the first few?" For the record, the answer is "none of them" and now I realize I should have just gotten up and walked out of that interview right there....
ETA - cross-posted with Neuro - he has very good advice.