I'll be impressed if someone can beat me on this. No lie: no puncture flats between September 2004 and June-ish 2010 (can't remember exactly the date). During that period I put about 6000 miles on a set of 700x25 Armadillos, 10,000 miles on a set of 26"x1.5" Armadillos, another ~5000 between some Schwalbe Marathons, two other sets of Armadillos, and some Vredestein Fortezza Tri Comps, and finally ~5000 miles on some Continental Grand Prix Four Season tires that finally punctured one day on the way to work last summer (tire went flat during the day). I've since punctured once more after another ~5000 miles running the same Continental tires (but a new pair after the first wore through to the cords after 6000 miles).
The 700x25 and 26x1.5 Armadillos were retired due to wear without ever allowing the tubes to be punctured. Impressive.
During that puncture-flat dry spell, I did flat two times. Once was due to a poorly installed tube in the 26" Armadillos. Somehow, I had the tube slightly twisted when I installed those tires and 6000 miles later it flatted on me at 10pm on a dark road. I also had a flat due to improperly installed rim tape under the tube in my Vredestein front tire. Luckily the tube let go while I was taking a nature break on a ride. Scared my wife who was standing next to the bike and had me really confused when I returned to a flat front tire.
And for the record, I've always carried tools/tube to repair a flat even though I rarely get the chance to use them.