A while back, I was asked the question in the title during a job interview, and it really threw me for a loop. I've worked long enough to have run into my fair share of conflict and have had the odd customer or co-worker that I didn't get along great with, but I'm a pretty mild-mannered engineer and genuinely can't recall a single time I've accidentally caused actual offence to somebody in the workplace, much less intentionally.
The closest I could think of on the spot was a rather complicated but true story involving a middle manager on the customer site, who I'm fairly certain was being bribed by the competition (this was in a 3rd-world country) and did his level best to sabotage the project in order to get our company out. At one meeting, after once too often hearing him disclaim all responsibility for something squarely in his area, I publicly pointed out that he wasn't being very helpful in solving the problem, at which he pretended to take offence and went squealing up the food chain. Fortunately I managed to pull some strings of my own, and we got him removed from the project instead.
Alas, my interviewer wasn't impressed.
I: So he just pretended to be offended?
Me: That's right.
I: No, I'd like to hear about when you actually offended someone.
At which I drew a complete blank and we moved on after some awkwardness; I got the distinct impression he didn't believe I had never offended anybody. (And no, I didn't get the job, although I doubt it was because of this.)
So how should you answer that question?
Update: I'm seeing a lot of answers that seem to equate offence with conflict. To me these aren't the same: if you want the project delivered yesterday, and I tell you it will take a week, we may have a conflict (which are inevitable at work), but neither of us has taken offence. Even in situations like the above, where an "enemy" wants me fired for political reasons, they're doing so rationally because I (or, rather, my company) threaten their interests, not because I've personally done anything to offend them. Am I overthinking this?