About 250 mg of caffeine (though this also depends, on course, on your size, and the amount varies from source to source but basically 2-3 cups) can cause effects of caffeine intoxication - stomach aches, tremors, increased heart rate, anxiety, insomnia. It's not fatal but I can tell you it's super unpleasant, and the reason I personally finally quit drinking coffee a about a month or six weeks ago. I usually only drank one cup a day, but on certain days when I was busy all day I would drink two or three, and end up with trembling hands by the evening. And then I'd have a terrible time trying to fall asleep with my heart pounding. (I was told by a person who is a psychologist that a large intake caffeine can mimic symptoms of severe stress and anxiety, which was certainly true for me.)
I have had a few cups since then, so I haven't given it up completely, but it's only about 10% of the amount I used to drink.
Julie