I would always be prepared to answer this question (at the very least): What was the "toughest" (most challenging, difficult, hardest, etc...) "thing" (task, job, problem, etc...) you've had to do in your life or career and how did you handle, overcome, challenge, succeed, etc...with it?
As a volunteer in a HR dept recently, I heard that question from the interviewers in some fashion just about every other day.