When things go wrong, you don’t want your vehicle running on empty. Its a good idea to keep your fuel tank half full for a number of reasons.
During an emergency, you may not be able to refuel when you need to. This could be due to a power outage, fuel shortage, civil unrest, or other factors. Gas stations normally only keep a limited supply of fuel on site, in an emergency this supply won't last long. However, fuel pumps run on electricity so if there is an extended power outage then nobody will be able to fill up.
Also, if an evacuation is called for (i.e., hurricane), you want to have enough fuel to get out of town and on your way to safety. The chances are you will be driving slower due to traffic and possibly idling for a long time. This will decrease fuel efficiency and reduce range, meaning you won't be able to go as far. Having your vehicle run out of fuel will make a bad situation even worse.
Listen, I am guilty of letting my tank get down to the last gallon or two so this is one piece of advice that I am implementing myself. My suggestion is that you start doing this now in order to save yourself from running out during an emergency. Sure, it means more frequent trips to the gas station but its a small price to pay for being more resilient.