Do grad schools google their students before acceptance? If I have an internet presence where I am published on some websites, would that affect my chances of getting into grad school? More specifically, do grad schools google their applicants before getting accepted for a PhD program? For example, if someone posted some defamatory things about me on some websites, would grad schools google me to find these things beforehand? And if they do find these defamatory things, how much does it affect my chances of getting in?
I have no doubt that some grad schools google applicants.  I'm pretty sure that defamatory things others say about you will have close to no effect on your admission.  It's the things you say yourself that might give you trouble.  If you're openly pro-nazi on your facebook page, that'll be a problem.  

And, unfortunately, if you take a bold public stand on one side of some issue (say the Palestinian state) and someone one the committee feels strongly the other way, it could still be a problem.  But don't worry about others' comments.  Everyone knows about trolls.