I give myself 30 minutes, minimum, (most days I ride to work, I'm here almost an hour early). Mostly, it's because I never want to hear my co-workers say, "He'd be on time, if he didn't ride that bicycle." Flats haven't made me late, yet.
I've only once had a catastrophic tire failure. I had to walk my bike about half a mile to the bus stop and did get to work on time. At lunch, a co-worker drove me to a bike shop.