A EMP would cause a disruption in the area that it occurred it would not effect the web anywhere else. The problem with a EMP is it would shut down everything that ran on electricity or battery. This is where it gets nasty. Without electricity and everything shutting down that area becomes a mob zone. People would think it is the end of days and probably go on a rampage. Not a good thing.
I am really intrigued by this subject and think talking about it here will lead off topic. So I am going to start a new topic and hope to learn more about these.
Someone once told me that nothing was impossible just highly improbable. I believe the person was quoting someone and was trying to be a smarty pants. I told that person to lift this mountain and throw it into the sea (me also being a smarty pants here as this is told that if you faith you can tell a mountain to lift himself and throw himself into the sea). Back to the topic. To take out the internet will require the effort that is not possible now. The most someone or a group can do now is disable internet in an area or zone by targeting the particular ISP in the area. Even the bigger ISPs have backups in place, so disabling will just be temporary anyway. EMP works on the principle of disrupting electricity itself not cutting off it's flow. So an EMP will only disrupt the internet by causing the server to shut down because of lack of power. Rerouting power back to them will cause them to run again. EMPs don't normally cause physical damage to components but the sudden disruption or should I say displacement of electricity has been known to damage sensitive electronic components. Again all of this is only temporary because these components are easily replaced. So in my view, nope it is not possible...at least not yet...
I do not think it could be effectively shut down world wide. One could wipe out all of ones countries activity or a time while causing major havoc as AlaskanLDS mentioned. I think EMP if properly harnessed could be one of the most devastating terrorist weapons created.
Mind you I have a bit of an evil trend in thoughts of shutting down most of North American in a matter of a few hours with the right planning. We are very vulnerable to say the least. Mostly because of our mind sets.
I now know how to shut down the entire internet. Global thermo Nuclear War. After that the only things that will be around to work correctly will be hand tools. We will not have to worry about the internet because we will be too busy trying to just survive. I do not believe anything short of this will shut down the world wide internet.