Jeeze, definitely some incredibly thoroughly prepared people here. Every non-mtb bike I own has a small pump (usually a topeak mini-morph) mounted under a bottle cage, and a small saddle bag with a multi-tool, spare tube, patch kit and chain link in it. If anything on the bike beyond that fails I have my cell phone to call for an emergency pickup. I can't remember the last time I needed to.
I still wear a hydration pack when riding mountainbikes, so I have a little more in that pack. Mountain morph pump, shock pump, a larger multi-tool (topeak Alien II), quick links, a tube, a small bottle of tire sealant and a small first aid kit. A spare derailleur hanger wouldn't be a bad thing to add, but honestly its been 15 years since I broke a hanger. Modern derailleurs are much more tucked in than old 8/9 speed stuff and I got pretty good at not banging it on things.