Depends on the car. When I frequently owned lots of beaters, some burned oil, some had very old coolant hoses, etc. So I carried extra water and anti-freeze, extra motor oil, etc. And at least twice I had to refill a coolant system on the road....so the extra gallons of water I carried came in handy. Again, it depends on your vehicle and how from home or civilization you are. One time in 1977 I was driving through Death Valley and was on the gas gauge "E" line. And essentially no small gas stations were open as it was Sunday. The last one I passed was at 1/4 tank and I figured I'd have plenty of choices further up. I limped 35 miles at or below "Empty" before getting a refill in the next big town. A gallon of gas in the trunk would have been nice...and peace of mind. I was only 23 then and not very "road wise."
When I did shows with my '69 Roadrunner at up to 300 miles away, I carried spare bottles of all the major engine bay fluids, brake, ATF, coolant, engine oil. You never know. And a few times I needed them. In fact I carried a barrage of spare parts for the car from an extra carb, distributor unit, alternator, voltage regulator, ballast resistor, plugs, wires, points, coil, and about every electrical item that could conceivably "kill" the car.
For a newer vehicle without any know issues, I wouldn't carry any extra fluid. But from experience, having a gallon of drinking water in the car comes in handy for drinking, cleaning off bird poo, emergency fills to washer reservoir or coolant in a pinch. Why wouldn't you carry that at all times?