But driving on empty, fretting about the nearest gas station, is not good for you. Range anxiety — it's not just for electric cars.
And it's not good for your car, either, because your in-tank fuel pump is cooled by the fact it's submerged. When you take the fuel level to the very bottom of the tank, the pump can overheat. It can also suck up sediment and clog your fuel filter. And if you kill the fuel pump by trying to save money, it'll cost you a lot more than what you managed to save looking for cheaper gas. The "E" in the gauge doesn't mean "Eh, keep driving."
For that reason and others, you shouldn't drive with less than a quarter of a tank, and preferably you should keep the tank full in case of emergencies — if you're fleeing a hurricane or a zombie apocalypse, you don't want to have to stop to gas up. And of course you don't want the engine to conk out while the car is in the middle of traffic or in an otherwise unsafe place.
That said, how far can you actually go with the needle showing empty? Let's say you're driving an unfamiliar car, and the fuel light comes on. How dire is your situation?
The website YourMechanic actually put together a chart with several recent model-year cars showing just how far they will go after the fuel light comes on. It's a rough approximation, because when the chart lists, say, a Ford Mustang, it doesn't specify which engine we're talking about. But the difference in driving distances from model to model tells you just how uncertain this whole business is.
And yes, there's quite a difference between models: With a 2015 Silverado you need to fill up 25 miles after the light comes on, but some cars like the Nissan Altima have three gallons left in the tank at that point, and you still have perhaps 100 miles. Though from experience, I'd say those last miles would be quite tense.