2 in the past two years.
One was a shredded tube caused by bad rim tape on a used bike I bought. At the time I only carried a patch kit, and there were far too many holes to patch. I had just left the university, so I rolled the bike back and took the bus home.
The other was a frozen freehub at about the half-way point of my commute. Rolled the bike over to a pay phone and called for a pickup.