He discovered the pencil eraser and carbonated water, essentials for Sudoku and Diet Coke, respectively.
Aside from those critical discoveries, his most important contributions to science had to do with the chemistry of air. He is generally known as the discoverer of oxygen, but it was Priestley who first proposed that air is not a single element (as in air, water, earth, and fire), but was made up of a mixture of gases.
Priestley may have been one of the first scientists to use mice in research. Using a candle, a mouse, and a sprig of mint, he demonstrated that oxygen (as it was later dubbed by Antoine Lavoisier) is needed to keep a candle alight and a mouse alive. He also showed that, although flames and mice use up oxygen, plants produce it. That's photosynthesis.
He discovered a lot of gases. Along with oxygen, there was carbon dioxide, carbon monoxide, ammonia, nitrous oxide (laughing gas), and hydrogen sulfide.
Hydrogen sulfide is the gas that give rotten eggs their rotten smell. High doses are lethal. A recent study has shown that when mice inhale small doses of hydrogen sulfide, their hearts and metabolisms slow down and their bodies use less oxygen. (Here's the paper.) It's like hibernation, but without the cold. Some also call it suspended animation. The effect is completely reversible with no apparent ill effects.
Hydrogen sulfide allows mice to survive in conditions of low oxygen. If it's true (and safe) for humans, too, then it could buy some precious time in the ER.
Back to the eighteenth century. Not only did Priestley demonstrate that oxygen kept mice alive, but more was better. Extra oxygen added to the glass chamber enhanced mouse survival.
"Had it been common air, a full-grown mouse, as this was, would have lived in it about a quarter of an hour. In this air, however, my mouse lived a full hour; and though it was taken out seemingly dead, it appeared to have been only exceedingly chilled; for, upon being held to the fire, it presently revived, and appeared not to have received any harm from the experiment."
He also tried some of this stuff himself and felt "peculiarly light and easy for some time afterwards." A man truly ahead of his time.