Consider the following not mentioned above:
* Spare tubes in old socks. Reduces wear and tear rubbing around in the bottom of the panniers / handlebar / seat bags and gives a nice place to wipe grease from your hands.
* Medical information and insurance card (in addition to personal ID). Not really a tool, but critical in some instances.
* I, personally, like a full-frame pump. My Topeak Morph just seems to take FOREVER to pump up the 20x1.75 tires on my Bike Friday, much less tje 650Bx38's on my main ride. But many others are just fine with the smaller pumps. (And don't simply rely on CO2 cartridges. Not helpful once you've pumped the tire up 3 or 4 times searching for the "oh, god, not another one to find" puncture and you've blown :-) through all your cartridges. I do recognize they may be necessary for seating tubeless set-ups though.)