You should think hard about how you can differentiate yourself from others -- every step of the way during the interview. Be memorable in a positive way even when answering these "boring questions." And, to be well-prepared to give smart answers to behavioral interview questions, read my article Smart Strategies to Answer to Behavioral Interview Questions
Example: “It was the first day of my boss’s two-week vacation and our agency’s highest-paying client threatened to leave because he didn’t feel he was getting the personalized service he was promised. I spent my lunch hour on the phone with him, talking through his concerns. We even brainstormed ideas for his next campaign. He was so grateful for the personal attention that he signed another six-month contract before my boss even returned from her trip.”

Example: “It was the first day of my boss’s two-week vacation and our agency’s highest-paying client threatened to leave because he didn’t feel he was getting the personalized service he was promised. I spent my lunch hour on the phone with him, talking through his concerns. We even brainstormed ideas for his next campaign. He was so grateful for the personal attention that he signed another six-month contract before my boss even returned from her trip.”
What your interviewer is really trying to do with this question—beyond identifying any major red flags—is to gauge your self-awareness and honesty. So, “I can't meet a deadline to save my life” is not an option—but neither is “Nothing! I'm perfect!” Strike a balance by thinking of something that you struggle with but that you’re working to improve. For example, maybe you’ve never been strong at public speaking, but you've recently volunteered to run meetings to help you be more comfortable when addressing a crowd.