I've been considering getting my own domain for email for some time -- the benefits are obvious. But I have one concern. If I use the address `mail@my-real-name.com`, does this pose a privacy threat? If someone wants to try and track my activities online, they can take that address, which is clearly tied to me (especially if, say, I use that domain for a blog too), and then go to ashleymadison.com (does that still exist?) and try a password reset for that address; many sites poduce differing responses to password reset requests depending on whether or not you have an account there. If the response is "We've sent a password reset link to that address", rather than "There is no account with that address", then people now know I'm a philanderer.
I've even heard of people writing a bot to do this across hundreds of sites; it's very interesting to see which C-level executives have been using their work accounts to access sites they shouldn't have.
The obvious advantage of having a GMail or Outlook address is that only Google or Outlook have to know who you really are; the address could be anything you want and doesn't have to be related to your real name. In addition, you can do as I do and have multiple addresses -- not the "throwaways" which people often speak of, but simply different addresses for different online activities -- so that if an account ever got compromised, there would be no way to link it to any other account.
Email security and privacy is a hard problem to solve.
