The goal of your answer is to communicate that you understand the importance of client relationships and that delighting a client leads to return business and often to new business from others in the client's circle. You want the interviewer to see that you will work hard by not only doing the work, but doing more than a client expected.

Choose an example that you can distill down to a good story. If you include too much unnecessary detail in your answer, the interviewer might lose interest. Focus on the situation, the expectation of what needed to be done, your actions and the final outcome. If possible, tie it back to how it impacted the business and the bottom line.

I think it is really important to go above and beyond for clients when possible. A good example of this is a recent brochure I created for a new client. The client needed the file delivered to their printer by noon that Friday to ensure the it could be printed and shipped on time. I uploaded the file to the printer's FTP site early that morning and sent them an email asking them to let me know they got the file. When I hadn't heard anything by 11:00 AM I called the printer and found out their server was down. I got in the car and personally drove it down to the printer because I knew it would damage my client's reputation if the brochures weren't delivered on time. The client was incredibly appreciative of my efforts and we've been working together ever since.