Why did Hamlet pretend to be insane?

I've read this play many times and it's one of my favorites. One of the questions I frequently ask myself is WHY did he chose to become insane? He could have committed the murder of Claudius much easier WITHOUT drawing attention to himself. I never understood why he chose to draw attention to himself by feigning madness, if indeed he chose to be mad at all (i.e he was really insane). Any ideas?