I keep a fanny pack around (for when I don't have enough pockets and to keep stuff in one place until I stuff my pockets ) with extra money, some ID, a cell phone, a couple of food bars, some Endurolyte tablets, a pair of rubber surgical gloves (for keeping your hands clean when fixing flats, putting chains back on etc.). Some guys keep a wad of duct tape, a few zip ties, and few other odd bits for on the road repair.
We've been using a fanny pack - we call them bum bags here in the uk as a fanny is a totally different animal to us - close but... 
Surgical gloves, duct tape etc, yep all good advice - will add to our stash.
See
http://www.bikeradar.com/gear/articl...repairs-18199/ for some interesting hints.
Thank you - will check this out next.
As for what breaks aside from getting flats ? Derailleur cables. Check them as part of your checkout ritual before you go out. When I was a teenager, a friend of mine had a cable snap while a bunch of us where doing a long climb in the middle of nowhere. We got him back on the road and had things working well enough but it would have taken a lot less time if I knew what I know now.
Will add this to our purchase list!
Anything else ? I always ride with gloves, usually the fingerless type but if it's cold I'll stuff a pair of full fingered gloves into a jacket pocket. One thing I should be carrying is an Epi-pen especially when I'm riding in unpopulated areas.