I take a spare inner, 3 leavers, multitool, money (always have at least £10 on me.) mini pump (spesh one - Really good! Says it can manage 90psi, but I've got it to 120 without getting cramp to badly) and couple of cola cubes in case I need something to munch on - All of this lives in my saddle bag, leaving just enough room for my keys and phone (though I don't put my phone in there - Don't want it scratched!)
I don't bother with puncture repair kits. Fix it when I get home.
I normally have another inner tube living in my seat post, but I had to use it

I think I will start carrying a bit of old tire in case I get a massive cash too.
Other than that, I don't see what else you need.
Obviously need some water and food depending on how far/fast your riding, and enough clothes to keep warm - but I like to think Im covered for most emergencies (other than a chain coming apart - Then Im buggered.)