Been doing it for decades with no cellphone. I carry two quarters for a pay telephone in my patchbox but there aren't any payphones anymore. Someday I need to get me a cellphone.
Don't be a dummy and ride far on rotten tires like I did last summer. Luckily I was only a few miles from home when one split. I used to carry a dollar bill too just for a tire boot but had forgotten about that after a decade layoff until a forum poster reminded me of that trick. I walked my bike for miles then took a chance riding about the last mile or so with the tube showing. It finally blew about 2 blocks from my house. Now I carry a couple of these tire boots:
Park Tool Emergency Tire Boot Set - Normal Shipping Ground
I always carry a chain breaker. Haven't used it myself but I've used it on a riding partner's broken chain once. We just shortened it and he stayed off his inside cog.
I also carry a spoke wrench. They come in handy in case you bend a wheel. You'd have to loosen the spokes all around and find a tree limb or something to bend it back with, standing on it, and re-true the rim with your bike upside down. I have the advantage of having built some wheels. It happened to me once when I slipped into a rain gutter about 30 miles or so away from home and I got back home OK. In fact I rode on that rim for about a month until building my present wheels.
I need to get me one of those cyclist dogtag IDs one of these days too with my address and blood type on them. I like to carry a map in a plastic bag too since I have no GPS device.