Is the whole world moving to Gmail?

I’m noticing more and more that everyone seems to be abandoning the traditional e-mail server in favor of Google’s Gmail. My Internet Service Provider switched over a while ago. Recently, I also joined a consulting group, working on managing and maintaining their Web site (and doing side Web work for them), and found that their e-mail is completely managed through Gmail. That Web site is hosted by GoDaddy. After a bit of research, it seems that Google and GoDaddy have (and have had for a few years) some sort of agreement that allows users to sign up for Google Apps and GoDaddy hosting all rolled into one.

In addition, I have heard that many colleges are now switching their student e-mail servers over to use Gmail rather than the services they have used in the past. In fact, the entire state system under which I work has moved over to Gmail for the student e-mail system. While our support staff e-mail is still hosted locally on an Exchange server, all student e-mail now runs through Gmail.

Is the whole world switching over to Gmail? Is anyone still using their own mail servers to handle sending and receiving correspondence? Does it even make sense to use your own server anymore? Will the world come to a grinding halt if Google’s e-mail servers ever shut down for any reason?