I take something to deal with anything on the bike I know how to fix. There are a few things that are too bulky and heavy that I don't fix. But just go over your bike and look at everything and ask yourself what you would do if it gave trouble. You either dont know how to fix it, won't be able to carry it, or you need to carry it. I should point out through careful equipment selection over the years the stuff I need to carry goes mostly in the palm of my hands. Try to get everything adjustible by allen wrenches, and just carry the keys your bike actually uses not the fancy tools with lots of heavy bits you won't use.
Tire wise I do carry a folding tire. One can go any time and when it does it will let you down in a big way. I can't always get the repalcement parts I want even in a big city, and it means a lot of wasted time. However, a lot of people don't take it this far, also it depends how bulletproof your tires are. I would rather carry a tire and run light ones than rotate dead weight all day. At least on blacktop tour.
For patching, I use instant stick patches, a Quick Stick for unzipping the tire, and a Road Morph pump for making inflation easy.
I carry light gloves to keep oil off my hands and other dirt.