I have only been pulled over a couple of times in the last few years, and they have not asked that.
Do not lower your window, giggle, order a bacon cheeseburger, French fries, and a large Diet Coke – then close your window and point and laugh with your friends.
Thinking back, I was pulled over for doing 43 in a 30mph zone when I was just on my R plates. The officer would probably have given me quite a spiel about driving too fast etc but Dad leaned over and said it was probably his fault for not keeping an eye on me and all that, the officer seemed convinced that I would be reprimanded later and gave me a warning, not a ticket.
I had one like that once - I was sitting, late at night, at a red light waiting to make a right turn. I was suddenly overcome with the insane notion that it would be fun to see exactly how fast I could pull away and make the turn. There were no other cars around, except the one behind me. The light turned green and with wheels spinning and screeching, I pulled away and turned - and as I turned, I could now see in my rear view mirror, the jam-sandwich red stripe down the side of the other car.
The police car pursued me with lights and sirens - I pulled over when it was safe and the police car swerved around me and stopped diagonally across my front. I stepped out (that was the advised action at the time here - it shows willingness to cooperate). Long story shorter - I was about 100 yards from home, the officer realised I had just done something stupid and impulsive, it was really late and I don’t think he wanted the paperwork. I was sent home with nothing more than a red face.
To the OP… I have no idea what would be the correct answer, but I would be inclined to say, in as non-confrontational and puzzled a tone as possible, “I’d like you to tell me, please, officer” - it admits nothing, and neither confirms or denies that you know or suspect the reason for being pulled over.
There is a serious point about police asking you to incriminate yourself (which is effectively what you’re doing).
When you get a speed-camera ticket in the UK, you are asked to confirm that you were the driver by completing a form to send back to the police.
A number of people have launced test cases in the UK to argue this is in violation of Police and Criminal Evidence Act (PACE), as it denies the right to silence and self-incrimination.
Basically, if you admit you were driving you get a fine and penalty points. If you refuse to admit you were driving, you get a minimum fine and points automatically.
So you’re buggered either way.
So far the courts have rejected this argument, but police saying “do you know why I stopped you?” is the same thing IMO.
In the UK (based on my viewing of “Police, Camera, Action!” etc) officers will tell you straight out why you’ve been stopped, rather than asking.
Speed cameras (we call them “red-light cameras,” although they are also used for speed limit enforcement) are controversial here, too, for a number of reasons: the company which operates them under contract to the city makes more money if they issue more tickets; you can’t confront any prosecution witness at trial since it’s an automatic camera, after all; and the city ordinance which authorizes their use characterizes such tickets as civil matters, although you can and more often than not will be fined and may get points against your license. Our state supreme court will probably have to eventually address all of the issues that these cameras have raised.
It’s the same answer to the question “does this dress make me look fat”. 
Seriously, though, I hardly ever ask people that. I have a little verbal judo line that I use:
PKB: " 'Afternoon, I’m Officer Beitz of the Metro police department. I want to see your drivers license please. The reason I pulled you over is because I clocked you with radar going 53 in this 30mph speed limit zone".
That answers who I am, what I want, and why I pulled you over in less than 5 seconds.
Another thing, if I’m going to cite someone I don’t give a lecture, and if I lecture them I don’t give a cite. Theres rarely a purpose in doing both. I write a lot of tickets, and I give even more warnings. Both have value, and there are a lot of factors in each individual stop that determines the outcome.
I was going through Norwich the other day, and saw a cop pull a U-turn to stop an out-of-state plate car. Yeah, they really mean it when they say 25 mph!! (I was warned about Norwich in particular when I first moved here. 
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Re: the “red-light cameras”
I was driving through NYC at about 4:30 am once, and accidentally ran a red light, and there were two gigantic FLASHes behind me, and I realized I had been photographed. Later, after sunrise, I drive back and easily saw where the camera was. About 6 weeks later, I received the legal stuff in the mail, including two time-stamped photos. Both showed my car, rear plate clearly readable, and the red light. One photo showed me in the intersection, and the other unarguably showed that the light was already red before I entered the intersection.
And the legal stuff explained that the law was written so that the fine is charged to the owner of the car, regardless of who is driving.
Thanks to everyone for the wonderful replies. Personally, I don’t recall ever being asked “Do you know why I stopped you?” The last time I got stopped was at night on a busy rural highway. I pulled over and turned on the interior lights so that the officer could see it was just me, my wife, and three kids. Since the lights were on, we couldn’t easily see out. I waited for the officer to appear at my window and it seemed to take an awfully long time. My wife turned, glanced out her window and nearly jumped out of her skin. The officer had been standing outside her window waiting for someone to notice him. He let me off with a warning (about speeding) because we were all laughing so much.
Thanks, Officer pkbites. That is exactly the sort of thing I would expect a professional officer to do.
I got a ticket from a red light camera in Chicago. I didn’t even know I had run the light until I got the letter in the mail several weeks later. The legal-eze said that it was a civil ticket, similar to a parking ticket, and points would not be added to my license. If I wished to contest the ticket I could go to court, but since I live more than 1000 miles from Chicago, it didn’t seem like a good bet. The photo evidence was pretty damning anyway. We don’t have red-light cameras in Texas, yet. I was in favor of them, but now I’m not so sure.