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.
Even if the graduate school itself doesn't officially 'google' you, you can be sure potential advisors will. It's just too easy and accessible. I'd assume they will, and do your best to clean things up, or even temporarily deactivate your account if you're that worried. I'd be less concerned with the defamation and more concerned with the overall first impression.
For each PhD student I advise, I have to raise roughly a half a million dollars of funding over the course of their degree. So, you'd better believe I Google any student I'm seriously thinking about taking on!
Typically, however, I am not looking for anything about their personal life; rather I am looking to see if there is any useful information about their potential as a grad student. For instance, some students these days post class projects online, blog about research, post interesting code to GitHub, etc. More often than not, the information I dig up this way is positive and only supports their application (and I wonder why they didn't include it in their application in the first place!).