I carry at least a patch kit, small pump, and tire levers on any ride; usually an extra tube as well. There's 3 different tire sizes among my collection of bikes and a mix of Schrader & Presta valves, so I have to keep in mind which bike I'm on!

Patch kits & spare tube got me by just fine until I moved to the Southwest, and encountered the dreaded goat heads for the first time while on my mountain bike. Both tires went flat instantly, must have picked 25 or 30 of their incredibly sharp little spines out of the tires over the next hour. I now have kevlar belts on the MTB.