Because they promised (and kept the promise) of gigabytes of storage. And because their performance and some elements of the UI were superior to Yahoo and Hotmail. Because it was a vanity thing to do. Because it is web accessible, so you can access it from a friend’s computer, a public terminal, so on.
But it is still pretty sucky. As with most Google’s products, the UX is less than desirable. JF says IMAP sucks, but so what? But IMAP is the best way to use a mail server from a full featured mail client. And Google’s IMAP is really, really bad because of their muddling their label system with IMAP folders.
It’s a mess. I have a Google Apps for Domains (free version) account to which I migrated all my mail from a self-run mail server. I have been thinking recently of migrating to a self-run Amazon EC2 or some such setup.