Been about 4,000 miles since I got my last flat. I run Schwalbe Marathon Plus tires on my LHT. Before I gave up on cheap tires from Nashbar (riding a hybrid at the time), I got flats once every month or two, more often when tread became worn. Since going with Vittoria Randonneurs (one set) and now my second set of Schwalbe MPs, I've had two flats in the last 7500 miles or so IIRC, the most recent being from a nasty construction staple that I would venture to say could have dealt a blow to a car tire.
Between the longer tread life and the peace of mind of not having to worry about flats, I am glad I spend the extra money on good tires.