Back before the turn of the century, it was common for most people to get their personal email through an account provided by their Internet service provider. But when you moved, or changed from Qwest to Comcast, or when the ISP was purchased and changed its domain name, your old email address vanished in a puff of smoke and you had to do one of those “Hi everyone, please update your address book” messages to everyone you know. And then, a few months later, you went to visit some website where you really wanted to sign in, but they only had your old email address and they insisted on sending confirmation messages to it.
And yet some people still use an email address they don’t control. Even when it’s from Gmail or Hotmail or Yahoo, it’s not yours. Someone could decide to cancel or suspend your account for a real or imagined violation of the service’s terms. Oh, it happens.
This is why I’m a firm believer in owning your own domain and creating your own email addresses. That way you’re not at the mercy of geography or someone else’s business model.
Over at ZDNet, I have a tutorial on how to connect your custom domain to Microsoft’s free and excellent Outlook.com service. You get to send and receive mail using an address you own, and no one can take it away or force you to change it.
And did I mention it’s free?
Details here:
Why I use Outlook.com for my custom email accounts (and how you can too)
Ed Bott (@ wordpress.com) 
I have both actually. Important correspondence, and the like, are on the proprietary domain. Open and non-essential are on a big name domain. Anonymity and security are the reasons for having both.
I have my own domain, but it’s a heck of a lot easier to give out a known domain for an e-mail address rather than trying to spell out something that someone has not heard of before, or explain what it is when you get a question about it. I’ll stick to large company services for e-mail. Had my e-mail address for almost 18 years, and I’ll probably go away before that well known domain does.