My worst was getting a flat on the way to work in February 2009 on a wet, snowy morning. I ran over a shard of glass that cut right through the casing. Getting a cold, wet tire off by the side of the road in the dark is a much harder exercise than doing it in a well-lit, warm, and dry garage! I (stupidly) ran my fingers inside the tire to make sure it was smooth so the new tube wouldn't get cut too and gashed my finger on the glass shard that had punctured the casing. So on top on repairing the tire, I got blood on my clothes and inside my gloves.

There are "good" flats, though. The kind that make a slow leak which doesn't get discovered until after you get home. Those are easy to deal with.