Nobody is sure since (last I checked) there have been no reports of someone dying from an overdose of caffeine. However, experiments have been done on rats which suggest that the lethal dose for a human is anywhere between 2 grams and 4 grams of caffeine in the system at once. For reference: a common cup of coffee has about 125 mg of caffeine in it. This means that having 20 cups of coffee in your system at one time would be pretty unsafe. At that point, the other side-effects would be so pronounced that the drinker would be losing any positive benefits for productivity.