Running out of gas

The basic reason is that when you're at the end of the gas in your tank, all of the little bits of crud that have accumulated are no longer floating in a large volume of liquid, but now in a much smaller volume making it more likely to suck some of them up.

Another reason is that a mostly empty tank is more explosive (a little counter-intuitive at first). Gasoline vapor is actually the explosive bit. When your tank is mostly empty, it has a lot of vapor in it. That's why the racing fuel cells have a tank with a bladder inside. As you use up the fuel, the bladder shrinks and doesn't allow room for the vapors. That is what makes fuel cells safer in a crash.