I've been riding now for abotu two years, and haven't had a flat before last night. PArt of the reason for my good luck so far is that I use fairly beefy tires (700x32 or 700x35) with a skin in them.
Until last night...
I had spent a few minutes at home, adjusting my rear brakes before the ride. They were grippy/stoppy enough, but the lever didn't spring back quickly enough after I pushed it in for my liking. So, some attention to the springs and cantilevers and such was in order.
Then I started riding. After about 3/10 of a mile, I pulled over because I heard a noise on every revolution of the rear wheel. Turns out the brakes were grabbing. Looking at the rear tire, I could see a spot where the sidewall was bulging right at the rim -- and the bulge was rubbing against the top of the brake pad. "Uh-oh," I said to myself, "that doesn't look good." Kept on riding, hit a bump about twenty feet later, heard a whoosh, and the tire had gone all the way flat.
The thing that surprised me when I got the bike home and changed the tire was that I couldn't find any sidewall problems! I had expected there to be a spot where the sidewall was stretched or torn or something -- no, it all looked fine. The tube itself has one hole, not the two I would expect from a pinch bite.