Other than flats...dropped chain. This usually happens when I haven't been a good girl and done my basic maintenance (wipe down chain, test shifting) before (or better, after) a ride. Inevitably, the black grease winds up on my face. Sometimes, also due to a lack of proper maintenance, I need to adjust the brakes - but that happens less frequently.

I honestly don't remember the last time I used my bike tool while out riding around. I figure that if I stop carrying it around, that will be the day that I'll end up needing it.