It depends on the ingredients in the energy drinks, and depends on what you consider too many. Too much caffeine can be dangerous as it's a neurotoxin at high doses; you'd need to drink a large amount in a short amount of time. Energy drinks have 2-3 times as much as a strong cup of coffee. It also depends on your regular tolerance for caffeine - the more you usually have, the more you would need to intake for the same effect. Too much sugar can also be dangerous over the long period as it can be a cause for diabetes. In addition, the energy drinks have a cocktail of other vitamins and minerals that are not regulated. Patients that have called for medical assistance after consumption have complained of irregular heart rate, tremors, stomach upset, dizziness, and more serious symptoms from seizures, psychosis, cardiac arrhythmias, and sometimes death.

There are quite a few medical professionals suggesting to stay away from energy drinks as they can be addictive (it's the caffeine), and some ingredients are not regulated by the FDA. Essentially, play it safe, and drink the serving size suggested on the packaging - often these can be half the size that you purchase.