Could you ever have too much web traffic?

Maybe this is a silly questions, but could you ever have too much traffic to your site? Would there ever be a scenario where you would want to not have people visiting your site. Granted, it makes sense that you would want as much targeted web traffic as you could possibly handle but what about general traffic. How do the search engines perceive it? I wish I knew more about how search engine optimization worked – but I don’t. And I am finding myself more and more overwhelmed by all the information available to help you optimize your site. So, what do you think?