Eh, I have really skinny road tires on my bike. My old tires, Yes they blew all the time probably about 1 a week. Just got new tires and out of about 250 miles I've ridden on them I haven't had a single problem.

Getting a flat really depends on how good of tires you have and how easy you are on them when you ride. The real change is going from that soft supple squishiness of fat mountain bike tires to hard and unforgiving road skinnies.