TOD
Been through it a few times, but only when the credit card company spots something suspicious and contacts me, either to find out that a charge was indeed legitimate or that I didn't know anything about it. Here's what's funny (ha ha ha): I just went through it with TWO (count'em) cards, not two weeks ago. The first seemed to be a case of them proactively changing a lot of people's account numbers and they sent out replacement cards with no hassle. On the second, I got one of those phone messages to call them, which usually means a security question has come up, and sure enough there was a charge for $1.60 made in some foreign land. I confirmed it wasn't mine, and they did the change and the card arrived yesterday.
Those two were completely painless. I remember a couple of other times several years back, one in which American Express spotted something and called me, and put me through the wringer proving they had the right person. It was weird -- because I had no proof of who THEY were, or why they were asking me questions but providing no information, it was all rather Kafkaesque -- and I was starting to yell at them and threatening to hang up and report THEM when they finally started talking, like, one human being to another. Now I know to expect a few minutes of grief when these things happen.
So, several times over the years...and I'm fortunate to have never suffered an actual loss. None of these were cases in which I knew that the card number had been stolen, like BK did. Each one seemed to be an instance of some store or other company's records having been compromised. Scary stuff, though. And it can be supremely aggravating, again, because the victim is put through more grief than the perp.