How important is one's GPA when applying for a PhD position?

Once your GPA is above a certain point, it is not a great predictor of your performance in a PhD program (the threshold is not sharp, but is different for different PhD programs). I know students with 3.6 GPA who were admitted to, say, Berkeley, and students with 4.0 GPA who were not. Other factors were considered more important. 

However, it would be incorrect to say that GPA does not matter, as a 3.0 GPA would in many cases prevent PhD admission.