It's one thing if the Internet had never been invented, but a collapse of the Internet would be a worldwide disaster. Almost everything hinges on this crucial network of information. The Internet is such a critical part of our daily lives that people tend to freak out over tiny disruptions in service.
It would take a global disaster to knock out the entire Internet. In the event of a solar flare, meteor strike, earthquake, or some other global event, the Internet could be gone as we know it. Major disruptions could also occur if some of the main cable lines or data centers were destroyed for some reason.
Another scary cause would be that the Internet eventually becomes overloaded and fragmented, which would make it unbearably slow and difficult to use.