This can vary and depend on your weight, gender, age and overall health. In general it is recommended that young adults do not comsume more than 400gr of caffiene per day. This equals about 4 cups (if you do not drink other caffeinated drinks, such as coke).
Consuming more can cause side effects, such as anxiety, irritability, sleep disturbance, rapid heart beat and gastric issues. Do note that some people are more sensitive to caffeine than others.