What was the total burn time of the rocket stages that launched New Horizons?
The flight log here seems to have a rough idea. I count a burn time of about 4m30s for the first stage, a total of 11m00s for the second stage (a Centaur engine, burned once for 2m30s to put it in a parking orbit and a second burn of 9m30s to get it out of Earth orbit), and 1m25s for third stage. Total burn time was approximately 17 minutes.
There were also five solid rocket boosters firing for about 1m40s immediately after launch, at the same time as the first stage. You could tack that on to the burn time if you want.
Nitpick: 2:30 + 9:30 = 12:00 , if one discounts relativistic effects. 
Oh, fine. 18 minutes total, then.
Thanks.
The probe has also made six course corrections while en route. I haven’t been able to find the total amount of time that the engines were firing for each maneuver, but it sounds like some of them are many minutes long.