Register your own domain and sign up for the free version of google apps. I have a gmail inbox for [email protected] but if I need to change services I just move the MX record and upload my backups elsewhere.
The free version of google apps has been discontinued. New users can no longer sign up for it.
You can, however, get a similar effect by forwarding all your mail to your Gmail account and configuring it to send mail as your domain email address (including using your SMTP server if necessary).
Definitely a wise move to use your own SMTP server, or you'll end up with "From: [email protected] on behalf of [email protected]"[1].
[1] http://gmailblog.blogspot.co.uk/2009/07/send-mail-from-anoth...
It has been hidden, but not discontinued. You can still create a trial Google Apps account, and then "downgrade" to free account with 10 user limit
Given Google's service shutdowns, dropped support for protocols, and the horror stories of seemingly accidental account closures with no recourse, I simply cannot trust Google with something as critical as my email.