Is it possible to crash or shut down the entire Internet?
No. The Internet as a whole is a collection of many independent networks controlled and maintained by different people, businesses, and governments. It is designed to be redundant: even if one portion of the network goes down, users should still be able to access all or some of the others.
It is still possible for the Internet to experience outages often caused by severe events such as large power outages and earthquakes. When large outages occur, a sizeable portion of the Internet or even an entire country may be affected. However, even these serious outages will not cause the Internet to shut down or crash. For example, in early 2007 Asia experienced a series of earthquakes that damaged undersea cables that caused wide Internet and phone-related issues in that part of the world. However, the remainder of the world still had access to the Internet.
Also, some governments can set up firewalls and other protection schemes to prevent users from accessing pages on the Internet or block access to the Internet. For example, in 2011 the Egypt government shut down the Internet several times during protests to prevent any information leaking out onto the Internet. However, even during this strict shut down, citizens were still able to find ways to access the Internet.