Two. I didn't get one today, however, I did have a major tire problem. I kept feeling a "bump-bump-bump." I thought maybe my back wheel was out of true. On the commute in, I thought my back wheel slid out on ice. However, on the commute home, I was feeling some handling issues also. I got off the bike and spotted a huge bulge in the sidewall of my tire. I decided to get back on and take it slow to the bikeshop. It was 6 miles away. When I got there, the owner and I looked over the tire. It looked like it was seperating from the rim. He told me that the kevlar bead was breaking. The tire was useless. I had to replace it. The tread was pretty much worn anyway... 2300 miles on the back tire. It was a continental grand prix 4 seasons. I replaced it with a specialized all condition armadillo (the only 28mm tire in stock)
I guess that almost counts as a flat... but I was able to keep riding, although... slow and carefully.