I carry a spare tube, a patch kit with at least 6 patches in it, an Alien multi-tool, and a pump.
I've had many flats over the years and multiple flats on a single ride. The only time I've ever had a tire problem I couldn't fix was a sidewall blow-out about three inches long. By an incredible stroke of luck, it happened a block from a bicycle store so I was able to buy a tire and tube and carry on my way.